Dynamic behavior and concentration distribution of granular sludge in a super-high-rate spiral anaerobic bioreactor

Bioresource Technology 111 (2012) 134–140

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Dynamic behavior and concentration distribution of granular sludge in a super-high-rate spiral anaerobic bioreactor Xiao-Guang Chen a,b,⇑, Ping Zheng b,⇑, Mahmood Qaisar c, Chong-Jian Tang b a

College of Environmental Science and Engineering, Donghua University, Shanghai 201620, China Department of Environmental Engineering, Zhejiang University, Hangzhou 310029, China c Department of Environmental Sciences, COMSATS University, Abbottabad 22060, Pakistan b

a r t i c l e

i n f o

Article history: Received 11 November 2011 Received in revised form 8 February 2012 Accepted 9 February 2012 Available online 17 February 2012 Keywords: Super-high-rate Spiral anaerobic bioreactor Dynamic behavior Concentration distribution Sensitivity analyzes

a b s t r a c t Dynamic behavior and concentration distribution of granular sludge is highly dependent on the ecological environment of microbial communities and substrate degradation efficiency along bed height. Both were modeled and verified through experiments in a super-high-rate spiral anaerobic bioreactor (SSAB). The sludge transport efficiency of upmoving biogas (kt,n1) displaying dynamic behavior of granular sludge in SSAB were predicted and found to be much lesser than of upflow anaerobic sludge blanket (UASB). The bed concentration distribution (Cm,n1/Cm,n) which represented concentration distribution of granular sludge were also quantitatively predicted in two feeding strategies. Parametric sensitivity suggested that kt,n1 was significantly influenced by spiral angle, outer radii of spiral rectangular channel, settling velocity of granular sludge and superficial liquid velocity (vl), while Cm,n1/Cm,n was affected by vl and superficial biogas velocity. In addition, some measures were also suggested to optimize designs and operations of such bioreactors. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Many full scale upflow anaerobic sludge blanket (UASB) and internal circulation (IC) reactors have been developed to represent the second and third-generation high-rate anaerobic bioreactors, respectively, and were employed to treat industrial wastewaters (Lettinga et al., 1991; Habets et al., 1997). Owing to the high liquid and biogas upflow velocities, drastic up and down movements of granular sludge occur in high-rate anaerobic bioreactors resulting in the washout of the granular sludge, and thus a decreased volumetric efficiency due to a very slow growth of anaerobic bacteria. The granular sludge washout from UASB reactor is a usual consequence of the high liquid and biogas up-flow velocities (Herbert, et al., 1989; Rozzi et al., 1988), and thus the volumetric loading rate (VLR) of UASB reactor is normally restricted to 10–20 kg COD (Chemical Oxygen Demand) m3 d1. A two stage UASB reactor called the IC reactor was developed by Paques in order to decrease washout of the granular sludge, whereby VLR of 35–50 kg COD m3 d1 could be loaded in the reactor (Pereboom and Vereijken, 1994), but the VLR of IC seemed to be difficult to be further improved. The preliminary laboratory scale studies (zheng et al., 2008; Chen et al., 2008; Chen et al., 2011) revealed that VLR, volumetric hydraulic loading rate, COD

⇑ Corresponding author. Tel./fax: +86 571 88982819. E-mail addresses: [email protected], [email protected] (X.-G. Chen). 0960-8524/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.biortech.2012.02.044

volumetric removal rate and volumetric biogas production rate (BPR) of super-high-rate special anaerobic bioreactor reached up to 306 kg COD m3 d1, 15.3 m3 m3 d1, 240 kg COD m3 d1 and 131 m3 m3 d1, respectively. Many researchers have focused on the high VLR and its influencing factors affecting the VLRs of high-rate anaerobic bioreactors, such as microbial granules (Mu, et al., 2008; Tay, et al., 2003), restart-up (Dong, et al., 2010), mixing (Brannock, et al., 2010), Dispersion (Pena, et al., 2006) and so on. However, only a few researchers have previously studied the distribution and behavior of sludge dynamics of anaerobic bioreactors (Buijs, et al., 1982; Heertjes and Van Der Meer, 1978). So far, the dynamic behavior and concentration distribution studies are still at their dawn. The present study tended to investigate bed dynamic behavior and concentration distribution of granular sludge in SSAB. Dynamic behavior of granular sludge refers to the sludge concentration change ratio determined by its intercommunication along bed height which is related to the ecological environment of microbial communities. While concentration distribution of granular sludge refers to the volatile suspended solids (VSS) concentration gradient which depends on the biomass distribution and the substrate degradation efficiency along bed height. The principal objectives of this study were to investigate dynamic behavior and concentration distribution of granular sludge model. Once developed and assessed through the experimental results, the model can be employed to analyze the effect of wake stream, backmix

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Nomenclature A a b Cm,n Cm,n1 Fw,n1 Fw0 ,n H km,n km,n1 kt,n kt,n1 kw L N R R S

cross-sectional area of the reactor column (bed), A = ab, m2 width of rectangular cross section in Fig. 2 , mm length of rectangular cross section in Fig. 2, mm sludge concentration (TSS) in DVn, kg m3 sludge concentration (TSS) in DVn1, kgm3 upmoving wake stream in DVn1, m3 h1 backmix stream in DVn, m3 h1 height of the spiral rectangular channel in Fig. 2, mm sludge transport constant, dimensionless sludge transport constants of wakes, dimensionless sludge transport efficiencies of the downwards fluid streams between DVn1and DVn, dimensionless sludge transport efficiencies of the upwards fluid streams between DVn1 and DVn, dimensionless the wake factor, dimensionless length of the straight rectangular channel in Fig. 2, mm spiral pitch number in Fig. 2, mm outer radii of the spiral rectangular channel in Fig. 2, mm inner radii of the spiral rectangular channel in Fig. 2, mm spiral pitch in Fig. 2, mm

SR vg vg,n1

parameters sensitivity, dimensionless superficial linear biogas velocity upwards, m s1 superficial linear biogas velocity upwards in DVn1, m s1 vl superficial linear liquid velocity upwards, m s1 vs settling velocity of granular sludge, m s1 vs,n superficial settling velocity of the sludge in DVn, m s1 Xb basic parameter value Xi different parameter values Yb basic values of kt,n1 or Cm,n1/Cm,n Yi kt,n1 or Cm,n1/Cm,n of different parameters A spiral angle in Fig. 2, 0 < a < 90° /g gas production, m3 h1 /g,n1 gas production in DVn1, m3 h1 /m,n downwards transport of sludge from DVn to DVn1, kg h1 /m,n1 sludge transport flux from DVn1 to DVn, kg h1 qn VSS of the granular sludge in DVn, mg L1 qn1 VSS of the granular sludge in DVn1, mg L1 DVn upper, middle and lower equal parts along the z axis in Fig. 2 and n = 3,2,1 DVnDVn1 from DVn to DVn1 or between DVn and DVn1 DVn1-Vn from DVn1 to DVn or between DVn1and DVn

stream, feeding methods, configuration parameters of SSAB on biomass distribution along bed height relating to the performance of the process. Especially this study is expected to help the optimization of the operations and designs of such bioreactors.

biogas tube 9

2. Methods

8

2.1. Experimental set-up

recycle tube

The schematic diagram of the experimental set-up was presented in Fig. 1. The SSAB consisted of the upper, the middle and the bottom parts, and the upper part comprised the separation zone with a three-phase separator, the middle part was the reaction zone with a spiral board (Fig. 1(6)) containing anaerobic granular sludge (Chen et al., 2010b); while, the bottom part was designated as the distribution zone. The main configuration parameters of SSAB were: bed (column) diameter (d) Ø100 mm, bed height (H0) 500 mm, separation unit diameter Ø280 mm and height 300 mm. The upper and lower diameters of three-phase separator were Ø50 mm and Ø180 mm, respectively. Total and working volumes of the reactor were 6500 mL and 4250 mL, respectively. The total height of reactor was 1000 mm. The SSAB was fed with synthetic wastewater. Wastewater was pumped into the reactor by peristaltic pump (Fig. 1(2)), and biogas was collected by three-phase separator into wet gas-flow meter (Fig. 1(9)). The temperature of the reactor was controlled between 29 °C and 31 °C.

effluent 7

6 2

4 5 4

influent tube 3 1

2

Fig. 1. Schematic diagram of experimental set-up. 1-influent tank, 2-water pump, 3-glass beads, 4-vavle, 5- anaerobic granular sludge, 6-spiral board, 7-three-phase separator, 8-water seal, 9-wet gas-flow meter.

2.2. Synthetic wastewater The reactor was fed with synthetic wastewater containing sucrose (6 000 mg L1), NH4Cl (330.0 mg L1), CaCl22H2O(100.0 mg L1), trace element solution according to Mahmood et al. (2007) (1.0 mL L1), nutrition solution (32 mL L1), which contained Yeast Extract 0.6 g L1, Beef Extract 0.6 g L1, Tryptone 1.8 g L1, MgSO4 0.22 g L1, KH2PO4 7.54 g L1. The NaHCO3 was used to satisfy alkalinity requirements and to adjust pH value (7.0–8.0) with its concentrations varying according to the VLR of

SSAB. The influent concentration was kept constant and the VLR was adjusted by controlling hydraulic retention time (HRT). 2.3. Analytical methods The superficial linear liquid velocity upwards (vl, m s1) was calculated by the influent volume in relation to influent time. The superficial linear gas velocity upwards (vg, m s1) was

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determined by gas flow meter (BSD 0.5, China), while vg could be calculated from the gas production volume in relation to gas production time. The settling velocity of granular sludge (vs, m s1) was determined by means of a batch settling column (diameter = 100 mm, height = 1000 mm), and vs could be calculated by the settling distance (keeping the settling velocity constant) in relation to influent time. The determinations of total suspended solids (TSS) and volatile suspended solids (VSS) were carried out through weighing method (China Bureau of Environmental Protection, 1997). 3. Dynamic behavior and concentration distribution modeling 3.1. Physical model A spiral rectangular channel existed in the reactor bed which was similar to a spiral pipe with a rectangular cross section (Fig. 2 (a)). The Fig. 2 (a) is simplified to the Fig. 2 (b) which is the straight rectangular channel placed at a three-dimensional coordinates (xyz-o) by straightening and flattening the spiral rectangular channel. Fig. 2 (c) suggests that some relationships existed among various parameters regarding the physical model of the spiral rectangular channel and the straight rectangular channel which were as follows:

a ¼ R  rðignoringthethicknessofspiralboardÞ; tg a ¼ S=pd; H ¼ S  NL ¼ H=sina

ð1Þ

where a and b represent the respective width length and length width (mm) of rectangular cross section; R and r represent the outer and inner radii (mm) of the spiral rectangular channel, respectively; S represents spiral pitch, mm; N is spiral pitch number; L is length of the straight rectangular channel, mm; H represents height of the spiral rectangular channel, mm and a represents spiral angle, 0 < a < 90°.

Fig. 3. Physical model for granular sludge dynamic behavior.

3.2. Mathematical model The simplified physical model was presented in Fig. 2 (b), the total height L was subdivided into upper, middle and lower equal parts along the z axis(DVn, n = 3,2,1). Fig. 3 represented the dynamic behavior of granular sludge analyzed between DV1 and DV2 or DV2 and DV3. The Fig. 3 showed that the transport power of sludge resulted from the upward fluid flow led by influent and the upmoving wake stream (Fw,n1, m3 h1) led by gas production. Consequently, this sludge transport flux (/m,n1, kg h1) from DVn1 to DVn(DVn1DVn) could be represented as:

/m;n1 ¼ km;n1 F w;n1 C m;n1

ð2Þ

where km,n1 represented the sludge transport constants of wakes, dimensionless; Cm,n1 was sludge concentration (TSS) in DVn1,

Fig. 2. Physical model for spiral zone of reactor.

X.-G. Chen et al. / Bioresource Technology 111 (2012) 134–140

kg m3. Fw,n1 was proportional to the gas production in DVn1, and the wake factor, kw, was the volume of liquid transported upwards per volume of gas produced. Therefore:

F w;n1 ¼ kw /g;n1

ð3Þ

where /g,n1 represents gas production in DVn1, m3h1, and with Eq. (2):

/m;n1 ¼ kw km;n1 /g;n1 C m;n1

ð4Þ

or with kt,n1 = kwkm,n1:

/m;n1 ¼ kt;n1 /g;n1 C m;n1

ð5Þ

Fig. 3 suggested that the downwards transport of sludge (/m,n, kg h1) from DVn to DVn1(DVn-DVn1), was caused on one hand by the settling of sludge and on the other hand by the backmix stream (Fw0 ,n, m3 h1) that replenished Fw,n1:

/m;n ¼ ðv s;n  v l ÞsinaAC m;n þ km;n F w0 ;n C m;n

ð6Þ

where vs,n represented the superficial settling velocity (m s ) of the sludge in DVn; vl was the superficial linear upwards fluid velocity (m s1) of influent; A was cross-sectional area of the reactor column (bed), A = ab, m2; km,n represented the sludge transport constant of dimensionless; and Cm,n represented sludge concentration (TSS) in DVn, kg m3. Because the backmix stream was generated by the upmoving fluid transport Fw,n1 = Fw0 ,n, Eq. (6) could be rewritten as:

137

atmospheric pressure is neglected (the total height of reactor is only 1000 mm), the /g,n1 can be expressed in the following form:

/g;n1 v g;n1 q DV n1 ¼ ¼ R 1n1 /g vg qn DV n dn 1

ð11Þ

where qn1 and qn represent the VSS of the corresponding granular sludge in DVn1 and DVn, respectively, expressed as mg L1. Anaerobic bioreactors have been widely used for the treatment of not only high concentration industrial wastewater but also low concentration domestic wastewater at various HRT due to their high operational efficiency even at high VLR (Seghezzo, et al., 1998). Thus, there are two common kinds of feeding methods when bioreactor is operated at super-high loading rate: high concentration and low flow (HCLF) for industrial wastewater or low concentration and high flow (LCHF) for domestic wastewater. When operating the reactor at HCLF, the sludge transport mass resulted from vl can be neglected because vl is much lesser than vs,n. Thus, Eq. (10) can be simplified to:

1

/m;n ¼ ðv s;n  v l ÞsinaAC m;n þ kw km;n /g;n1 C m;n

ð7Þ

or with kt,n = kwkm,n:

/m;n ¼ ðv s;n  v l ÞsinaAC m;n þ kt;n /g;n1 C m;n

ð8Þ

In a stationary condition, neglecting the effluent sludge stream and the growth of the sludge, the upstream and downstream sludge concentrations are equal, so Eqs. (5) and (8) may be combined to obtain:

kt;n1 /g;n1 C m;n1 ¼ ðv s;n  v l ÞsinaAC m;n þ kt;n /g;n1 C m;n

ð9Þ

Thus, substituting the relationship A = ab into Eq. (9) and rearranging yields, the dynamic behavior and concentration distribution of granular sludge model of SSAB are as follows:

C m;n1 ðv s;n  v l Þsinaab 1 kt;n ¼  þ kt;n1 /g;n1 kt;n1 C m;n

ð10Þ

or

C m;n1 2pRðR  rÞðv s;n  v l Þsinatg a 1 kt;n ¼  þ /g;n1 kt;n1 C m;n kt;n1

ð100 Þ

or

C m;n1 ðR  rÞ sinatg a ðv s;n  v l Þ kt;n ¼2  þ R C m;n kt;n1 v g;n1 kt;n1

ð1000 Þ

where kt,n1 and kt,n represent the sludge transport efficiencies of the upwards and downwards fluid streams between DVn1 and DVn, respectively, dimensionless; vg,n1 represents the superficial linear biogas velocity upwards in DVn1, m s1; /g,n1 can be calculated from the overall measured gas production (/g, m3 h1) if the amount of substrate in DVn (n = 1, 2 or 3) being converted into gas is known. However, the substrate conversions into DVn is very difficult to be measured. In this study, considering the recycle ratio of 20:1 allowed in SSAB fairly high (Fig. 1), it is assumed that the fluid possesses even substrate concentration distribution along the bed height, and the microorganisms are similar in DVn. The substrate conversion is proportional to the biomass and the gas production rate depends on substrate conversions Therefore, the gas production rates were proportional to VSS of the corresponding granular sludge i.e. biomass in DVn. Thus, if the gas volume affecting

C m;n1 ðR  rÞsinatg a v s;n 1 kt;n ¼2  þ C m;n R kt;n1 v g;n1 kt;n1

ð12Þ

As shown in Eq. (12), the bed concentration distribution (Cm,n1/ Cm,n) of granular sludge in SSAB is plotted as a linear function of 1/ vg,n1 when employing HCLF. The slope of the line is related to vs,n, kt,n1, a, R and r. The value of kt,n1 can be derived from the slope of the line. The intercept of the line is the sludge transport efficiency ratio of downflow liquid and upmoving biogas, kt,n/kt,n1. By extrapolation to 1/vg,n1 = 0, the value of kt,n/kt,n1 can be found, and thus, by means of kt,n1 also kt,n. From Eq. (10), the bed concentration distribution (Cm,n1/Cm,n) of granular sludge in SSAB is not only related to vg,n1, vs,n, a, R, r, kt,n and kt,n1, but also vl when employing LCHF. 4. Results and discussion The present study involved HCLF strategy in SSAB with the COD value of 6500 mg L1 while the range of vl was from 0.021  103 m s1 to 0.069  103 m s1. Eq. (12) suggested that the kt,n and kt,n1 were two important dynamic behavior parameters. The slope and intercept of line must be firstly obtained according to the linear regression analysis of Cm,n1/Cm,n and 1//v,n1 before the values of kt,n and kt,n1 were known. The experiment data were shown in Table 1. Cm,n1/Cm,n could be calculated by substituting Cm,1, Cm,2 and Cm,3, while 1//v,n1 could be calculated by using Eq. (11) and substituting q1, q2 and q3. The linear regression analysis of Cm,n1/Cm,n and 1//v,n1 was carried out with parameters like R = 100 mm, r = 15 mm, a = 25.5°. Thus, the dynamic behavior and concentration distribution models of granular sludge of DV3DV2 and DV2DV1 were simplified to Eqs. (13) and (14):

C m;2 =C m;3 ¼ 0:05114ð1=v g;2 Þ þ 0:82594ðR2 ¼ 0:7796Þ

ð13Þ

C m;1 =C m;2 ¼ 0:04054ð1=v g;1 Þ þ 0:75111ðR2 ¼ 0:9122Þ

ð14Þ

Fig. (4) depicted a reasonable agreement (the correlation coefficient R2 = 0.7796 and 0.9122) existing between the experimental data and the derived Eqs. (13) and (14). Therefore, the models of dynamic behavior and concentration distribution of granular sludge were effectively developed. To exploit full advantage of these models (Eqs. (10), (100 ), and (1000 )) and to enrich the results of this study, LCHF strategy (not in practical use), was also simulated further in SSAB according to these models.

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Table 1 The experiment results and model parameters. Casea

1 2 3 4 5 a

/g(103m3/h)

vl(103m/s)

6.13 4.92 4.06 4.00 2.35

0.048 0.055 0.069 0.021 0.039

vs,n (103m/s) vs,2 vs,3

qn (kg/m3) q1

q2

q3

Cm,1

Cm,2

Cm,3

kt,1

kt,2

kt,20

kt,3

28.5 24.5 16.2 12.1 35.8

61.06 54.30 20.42 88.83 51.29

55.16 53.30 20.36 81.08 53.40

63.61 57.05 22.64 111.74 48.33

99.87 98.74 70.44 133.23 84.93

93.73 92.05 66.12 128.71 80.97

101.99 95.95 66.63 152.19 77.66

0.2444 0.2025 0.1460 0.1018 0.3157

0.2019 0.1673 0.1206 0.0841 0.2607

0.2015 0.1733 0.1146 0.0856 0.2532

0.1514 0.1301 0.0861 0.0643 0.1902

43.2 35.8 25.8 18.0 55.8

Cm,n(kg/m3)

kt,n(m3/m3)

Each case was steadily run about a week.

1.4

Cm,n-1/Cm,n

1.2 1.0 0.8 0.6

Cm,2/Cm,3

0.4

Cm,1/Cm,2

0.2 0.0

0

1

2

3

4

5

6

7

8

9

10 11

1 vg ,n −1 (s/m) Fig. 4. Mathematical model of granular sludge dynamic behavior.

4.1. The dynamic behavior of granular sludge Derived from Eq. (13), the slope and intercept were 0.0511 and 0.8259, respectively. Together with R = 100 mm, r = 15 mm and a = 25.5°, kt,n1 of DV3DV2 could be computed as 0.1018– 0.3157 m3/m3 (sludge/biogas) when vl = 0.021  103  0.069  103 m s1 and vg = 0.0832  103  0.2169  103 m s1. From Eq. (14), the slope and intercept were found to be 0.0405 and 0.7511, and similarly kt,n1 of DV2  DV1 was computed to be 0.0856–0.2532 m3/m3 (sludge/biogas) when vl = 0.021  103  0.069  103 m s1 and vg = 0.0832  103  0.2169  103 m s1. Thus, kt,n1 was 0.0856–0.3157 along the bed height. The results suggested that the sludge transport efficiency of downflow liquid (kt,n) was lesser than the sludge transport efficiency of up-moving biogas (kt,n1) and the sludge transport efficiency ratios (kt,n/kt,n1) of DV3DV2 and DV2DV1 were 0.8259 and 0.7511, respectively. Van der Meer (1982) reported that the kt,n/kt,n1 of UASB reactor reached up to 3.0 ± 0.9; while, kt,n1 reached up to 20.2 ± 2.1 m3/ m3(sludge/biogas) for sludge bed and sludge blanket. By contrast, the kt,n/kt,n1 and kt,n1 of SSAB were much lesser than of UASB. It could be due to following main reasons: (a) According to Fig. 2(b) and Eq. (1), L = 2.32 H when spiral angle was a = 22.5°. It was obvious that the ratio of bed height to its diameter was longer and therefore, sludge transport with ascending wake stream was restricted along the bed height. (b)In case of upwards transport of the granular sludge caused by ascending wake stream, two component forces developed due to the spiral board. Therein, one parallel component force with the parallel direction of the spiral angle was 0.43 (sina) times of the original upwards forces and the other perpendicular component force whose direction was perpendicular to the spiral board was 0.90 (cosa) times to that of original value. The parallel component force caused 57 percent decrease in the power responsible for the upwards sludge transport and the perpendicular component force partly responsible for sludge recirculation following the original path, and hence weakening the

sludge transport along the bed height. (c) A thin layer of biogas was easy to develop at the top of spiral channel by collecting the ascending biogas. The developed thin biogas layer accumulated majority of gas bubbles and freely rose along the spiral channel, but did not transport the sludge. Thus, the sludge transport flux was also weakened. Consequently, the spiral board in SSAB was responsible for providing foundation to fix the microorganism and optimized its ecological environment along spiral channel. In contrast, due to the larger value of kt,n/kt,n1 and kt,n1, the UASB reactor was easy to form short flow, dead space and completely mixed flow, which may be the major bottleneck in further improving the VLR of UASB reactor. 4.2. The concentration distribution of granular sludge During HCLF (vl = 0.021  103  0.069  103 m s1, 3 vg = 0.0832  10  0.2169  103 m s1) of SSAB, based on Eqs. (13) and (14), the ranges of Cm,n1/Cm,n of DV3DV2 and DV2DV1 were 1.0617–1.4406 and 0.9380–1.2384, respectively, as shown in Fig. 5 (a and b). Thus, Cm,n1/Cm,n were 0.9380–1.4406 along the bed height at HCLF. Fig. 5 (a and b) also depicted that Cm,n1/Cm,n negatively correlated with vg. For LCHF of SSAB, to compute the concentration distribution of granular sludge based on Eq. (1000 ), the vs,n, kt,n1 and kt,n/ kt,n1(n = 3 and 2) must be known. vs,n for LCHF employing the mean value for vs,2 of 23.4  103m s1 in Table 1. Eqs. (12), (13) and (14) were combined and 0.1324 m3/m3 for kt,2 in DV3DV2, 0.7511 for kt,3/kt,2 of DV3DV2, 0.2020 m3/m3 for kt,1 in DV2  DV1 and 0.8259 for kt,2/kt,1 of DV2DV1 were computed. Substituting these parameters and employing R = 100 mm, r = 15 mm, a = 25.5° into Eq. (1000 ), the models for dynamic behavior and concentration distribution of granular sludge of DV3DV2 and DV2DV1 were simplified to Eqs. (15) and (16):

C m;2 =C m;3 ¼ ð0:04054  1:1356  103 v l Þ=v g;1 þ 0:75111

ð15Þ

C m;1 =C m;2 ¼ ð0:05114  2:1855  103 v l Þ=v g;2 þ 0:82594

ð16Þ

Eqs. (15) and (16) could be used to predict the concentration distribution of granular sludge during LCHF operation of SSAB. When feeding wastewater at LCHF in SSAB, the upper limit of vl must be less than the settling velocity of the sludge (vs). It was presumed that if lower limit of vl was 0.069  103 m s1, the upper limit of vl was 23.4  103 m s1 (the mean value for vs,2) and vg = 0.0832  103  0.2169  103 m s1 (the same to HCLF), the resulting concentration distribution of granular sludge at LCHF was presented in Fig. 5(c and d). Fig. 5(c and d) suggested that, Cm,n1/Cm,n was affected not only by vg but also vl, and the ranges of Cm,n1/Cm,n in DV3DV2 and DV2DV1 were 0.8155–1.2374 and 0.8259–1.4388, respectively. Thus, Cm,n1/Cm,n was 0.8155– 1.4388 along the bed height at LCHF. It was obvious that the change range of Cm,n1/Cm,n at LCHF was greater than that at HCLF because the influence of vl was not neglected at LCHF, which indicated that the change of Cm,n1/Cm,n should be carefully

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1.4

1.4

1.2

1.0

0.8 0.100 0.125 0.150 0.175 -1

vg (10 m·s )

0.05 0.06

0.200

0.04 -3

0.8

0.6

0.6

0.100 0.125 0.150 0.175

-1

-3

vl (10 m·s )

-1

vg (10 m·s )

(a)

0.05 0.06

0.200

0.04

0.03

vl (10-3 m·s-1)

(b)

1.4

1.0

1.2

Cm,2/Cm,3

1.2

1.4

1.0

0.8

0.10 0.12

20 0.14

0.8 0.100 0.125 0.150 0.175

0.6

15 0.16

10 0.18

vg (10-3 m·s-1)

5

0.20

vl (10-3 m·s-1)

Cm,2/Cm,3

-3

0.03

Cm,2/Cm,3

Cm,2/Cm,3

1.0

1.2

vg (10-3 m·s-1)

(c)

0.200

5

10

15

20

0.6

vl (10-3 m·s-1)

(d)

Fig. 5. Concentration distribution of granular sludge. (a) Feeding at HCLF (4V3  4V2); (b) Feeding at HCLF (4V2  4V1); (c) Feeding at LCHF(4V3  4V2); (d) Feeding at LCHF (4V2  4V1).

administered when enhancing vl by increasing the recycle ratio of effluent or shortening HRT of the influent. Fig. 5 (c and d) also depicted that Cm,n1/Cm,n negatively correlated with vl and vg. 4.3. Parametric sensitivity analyzes According to Eqs. (100 ) and (15), the sensitivity analyzes of main parameters (X) such as vs, vl, R, a for kt,n1 and vl, vg for Cm,n1/Cm,n were performed on the basis of the following baseline values: vs = 0.03 m s1, vl = 10.00  103 m s1, vg = 0.15  103 m s1, R = 50 mm and a = 25.5°, r = 15 mm. 0.0606 m3/m3 of kt,n1 value and 1.0212 of Cm,n1/Cm,n value were gained by Eqs. (100 ) and (15) and regarded as respective baseline values, where each parameter varied within a range of ± 50%. Considering vs = 0.0150.045 m s1, vl = 5.00  10315.00  103 m s1, vg = 5.00  10315.00  103 m s1, R = 2075 mm and a = 12.7538.25°, sensitivities (SR) of kt,n1 or Cm,n1/Cm,n could be calculated using Eq. (17) in the following form (Chen et al., 2010a):

SR ¼

Y i  Y b Xi  Xb = Yb Xb

ð17Þ

where SR represented sensitivity (dimensionless); Yi is kt,n1 or Cm,n1/Cm,n of different parameters; Yb represented the baseline values of kt,n1 or Cm,n1/Cm,n; Xi represented the different parameter values and Xb represented the basic parameter value. Based on Eq. (17), parametric sensitivities of kt,n1 and Cm,n1/Cm, in proportion to the absolute value of parametric slope, were depicted in Fig. 6 (a and b), respectively. For kt,n1, the sensitivity of a was the maximum, followed by R and vs, while vl was the minimum (Fig. 6 (a)), suggesting that, for maintaining the stability of process, the sludge transport efficiency should be decreased by optimizing the configuration of SSAB when designing the process; for instance, reducing the spiral angle a prior to radius R. For Cm,n1/Cm,n, the sensitivity of vg was the maximum followed by vl (Fig. 6 (b)), implying that, for maintaining the high efficiency of process, the effect of vl on the sludge concentration distribution was less than that of vg, thus the manipulators should improve the VLR of such bioreactors (UASB, Expanded Granular Sludge Bed, IC reactors etc.) by rapidly increasing vl, it may involve increasing the recycle ratio of effluent or shortening HRT of influent. For instance, a high nitrogen removal rate of 74.3–76.7 kg N m3 d1, 3

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Fig. 6. Parametric sensitivity analysis. (a) for sludge transport efficiency(kt, n  1); (b) for sludge concentration distribution(Cm,n  1/Cm, n)

times of the previously reported top value was revealed by shortening HRT (0.16–0.11 h) by Tang, et. al (2011). 5. Conclusion The models presented for the description of dynamic behavior and concentration distribution of granular sludge were developed through mass balance of upstream and downstream biomass in SSAB. The sludge transport efficiencies of upmoving biogas in SSAB was much lesser than that in UASB reactor due to the spiral board in SSAB. The quantitative values of bed concentration distribution in SSAB were obtained in two feeding strategies. From parametric sensitivity analysis, kt,n1 was significantly influenced by a, R, vs and vl, and Cm,n1/Cm,n by vg and vl, which might help to optimize the operations and designs of such bioreactors. Acknowledgements This work is partially supported by the High-Tech Research and Development Program (863) of China (2009ZZ06311), the Science and Technology Pillar Program of China (2008BADC4B05), the Major Scientific and Technological Project of Zhejiang Province (2010C13001), the Fundamental Research Funds for the Central Universities and the Shanghai Leading Academic Discipline Project (B604). References Buijs, C., Heertjes, P.M., Van Der Meer, R.R., 1982. Distribution and behavior of sludge in upflow reactors for anaerobic treatment of wastewater. Biotechnology and Bioengineering 24 (9), 1975–1989. Brannock, M., Wang, Y., Leslie, G., 2010. Mixing characterization of full-scale membrane bioreactors: CFD modeling with experimental validation. Water Research 44, 3181–3191. Chen, J.W., Tang, C.J., Zheng, P., 2008. Performance of lab-scale SPAC anaerobic bioreactor with high loading rate. Chinese Journal Biotechnology 24 (8), 1413– 1419 (in Chinese). Chen, X.G., Zheng, P., Ding, S., Tang, C.J., Cai, J., Lu, H.F., 2011. Specific energy dissipation rate for super-high-rate anaerobic bioreactor. Journal of Chemical Technology and Biotechnology 86 (5), 749–756.

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