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Effect of supplementary carbon addition in the treatment of low C/N

high-technology industrial wastewater by MBR

Mathava Kumar

a

, Pei-Yun Lee

b

, Toshikazu Fukusihma

c

, Liang-Ming Whang

c,d,e

, Jih-Gaw Lin

b,⇑

a

Department of Civil Engineering, National Institute of Technology Calicut, Kozhikode, Kerala 673601, India

b

Institute of Environmental Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan

c

Department of Environmental Engineering, National Cheng Kung University, No. 1, University Road, Tainan 30701, Taiwan

d

Sustainable Environment Research Center (SERC), National Cheng Kung University, No. 1, University Road, Tainan 30701, Taiwan

eResearch Center for Energy Technology and Strategy (RCETS), National Cheng Kung University, No. 1, University Road, Tainan 30701, Taiwan

a r t i c l e

i n f o

Article history:

Received 14 October 2011

Received in revised form 21 December 2011 Accepted 21 December 2011

Available online 27 December 2011 Keywords: Membrane bioreactor Supplementary carbon Wastewater treatment Denitrification C/N ratio

a b s t r a c t

The effect of supplementary carbon addition for the treatment of high-technology industrial wastewater in a membrane bioreactor (MBR) was investigated. The MBR was operated for 302 days under different C/N ðBODL=NHþ4-NÞ ratios, i.e. 0.9–1 to 20 days, 1.6–21 to 42 days, 2.9–43 to 82 days, 3.6–83 to 141 days,

4.8–165 to 233 days and 9.3–240 to 302 days. Irrespective of the C/N ratios investigated, SS and BOD5

removal efficiencies were above 95% and above 80% COD removal efficiency was observed. In addition, complete nitrification was observed throughout the investigation. However, denitrification and total nitrogen removal efficiencies reached their maximum values at the highest C/N ratio (9.3) investigated. Real-time PCR analysis revealed 10 times higher ammonia oxidizing bacteria to total bacteria ratio under the highest C/N ratio condition (9.3) compared to the low C/N ratio condition (1.6).

Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction

High-technology industries play a very important role in the economic system of Taiwan. In Hsinchu Science Park, semiconduc-tor and optoelectronics are the main industries. These industries play greater role in Taiwanese economic development; neverthe-less, wastewater produced in these industries is complex and haz-ardous. In order to meet the effluent disposal standards in the science park, the wastewater is pretreated in the respective indus-tries before its discharge. Subsequently, the pretreated wastewater is collected into wastewater treatment plant. The SS, COD, BOD5

and NHþ

4-N of wastewater were around 100, 100, 50 and 60 mg/

L, respectively. Carbon to nitrogen ratio of the wastewater is very low, which has an impact on total nitrogen removal in the biolog-ical nutrient removal process (BNR).

Membrane bioreactor (MBR) technology is the combination of membrane filtration and activated sludge process. The secondary clarifier of conventional activated sludge (CAS) process is replaced by membrane module. The advantages of MBR include operation at higher mixed liquor suspended solids (MLSS) concentrations, re-duced sludge production, independent control of solids and hydraulic retention time (SRT and HRT, respectively), compact

and modular system requirement (i.e. small plant foot print), excellent performance and effluent quality (Judd, 2008). Since the MBR can be operated under longer SRT’s, nitrification could be more effective and complete due to the space for the growth of nit-rifiers. Moreover, carbonaceous organic matter removal efficiency is also excellent in MBR. Besides, the MBR can be modified with anaerobic, anoxic and oxic operations. Recent years, MBR is widely used in many countries owing to its elastic manipulations and excellent effluent quality. The MBR market value doubled in the 5 years between 2000 and 2005 to reach $217 and is expected to increase its market value from $296 million in 2008 to $488 mil-lion by 2013. Besides, the MBR technology is also efficient in treat-ing numerous small domestic wastewaters apart from industrial and municipal wastewaters (Kraume and Drews, 2010; Santos and Judd, 2010).

Conventional biological nitrogen removal process utilizes the activity of nitrifiers and denitrifiers for removing nitrogen from wastewater. As a first step in nitrogen removal, NHþ

4-N is

trans-ferred to NO

3-N by nitrifiers under aerobic condition and

subse-quently, NO

3-N is transferred to N2 by denitrifiers under anoxic

condition. Several factors can affect directly the biological nitrogen removal efficiency, one of the most critical parameters is C/N ratio. Theoretically, the stoichiometric C/N ratio required for the denitri-fication process is 2.86 ðCOD=NO

3-NÞ. However, some authors

re-ported that the practical C/N ratio required is greater than 2.86 in a combined nitrification/denitrification system. In anoxic/oxic

0960-8524/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.biortech.2011.12.102

⇑Corresponding author.

E-mail addresses:mathav@nitc.ac.in, mathavakumar@gmail.com(M. Kumar), whang@mail.ncku.edu.tw(L.-M. Whang),jglin@mail.nctu.edu.tw(J.-G. Lin).

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MBR (A/O MBR), The TN removal efficiency reached around 80%, when the C/N ratio of the system was maintained greater than 8 (Fu et al., 2009a,b; Tan and Ng, 2008).Carrera et al. (2004)have re-ported that complete denitrification was achieved when the C/N ratio was greater than 7.1 in pre-denitrification process. Choi et al. (2008)treated wastewater by intermittently aerated MBR (IAMBR) and observed that the TN removal efficiency reached a maximum of 89.1% when the C/N ratio was controlled at 7. The IAMBR experiment was also carried out by Yeom et al. (1999), where they obtained 90.7% TN removal efficiency at a C/N ratio of 11.6. Although the nitrifiers use inorganic carbon as electron do-nor, the C/N ratio still has influence on nitrification because of the growth competition between nitrifiers and heterotrophic microor-ganism.Komorowska-Kaufman et al. (2006)reported that nitrifica-tion is more stable when the C/N ratio less than 4 and reported a maximum TN removal efficiency of 95% at the stable condition.

In our previous study, we identified complete nitrification of the high-tech industrial wastewater in MBR without extra carbon source addition. However, the NO

3-N concentration in the effluent

was around 60 mg/L, which reveals that denitrification has not taken place. This is likely due to the characteristic of low C/N high-tech industrial wastewater. Therefore, the main aim of this investigation is to study the influence of C/N ratio in the treatment of low C/N high-technology industrial wastewater in a MBR sys-tem. The experiments were carried out under different C/N ratios of the wastewater in a pilot of anoxic/oxic (A/O) MBR.

2. Methods

2.1. Membrane bioreactor

A pilot scale A/O MBR was constructed in the premises of the wastewater treatment plant (WWTP) of Hsinchu Science Park in Hsinchu, Taiwan. The MBR system consists of anoxic and mem-brane tanks of 576 L and 1344 L capacity, respectively. The sche-matic diagram of the MBR is shown inFig. 1. A submerged MBR module made up of PVDF (polyvinylidene difluoride) hollow fiber with a pore size of 0.05

l

m and a membrane area of 3 m2was in-stalled in the membrane tank. The feed water was pumped into the anoxic tank for denitrification and subsequently routed into the membrane tank for nitrification. The mix liquid suspended solids were recycled between aerobic and anoxic tanks with a recircula-tion ratio of 2.9 Q. Permeate from the MBR was withdrawn for 15 min, followed by settling and back wash times of 1 min each. During settling of solids no permeate outflow and back washing were done, which is useful for the physical relaxation of the mem-brane and also for relax cleaning of the solids by the memmem-brane it-self on its surface pores to certain extent. The operating cycle was automated by a programmable logic controller.

2.2. Operating conditions of the MBR

The pretreated high-technology industrial wastewater using the coarse screen was fed into the anoxic tank first. The characteristics of the high-technology industrial wastewater used in the present study are shown in Table 1. The flow rate were 14.85, 13.97, 13.47, 15.24, 13.83 and 15.06 m3/day for days 1–20, days 21–42,

days 43–82, days 83–141, days 165–233 and days 240–302, respectively. Mix liquid suspended solid from the anoxic tank was pumped into the aerobic MBR tank. The total HRT of the wastewater in the MBR system (including anoxic and aerobic tank) was controlled at 3.2 h. The effluent from the MBR system was ta-ken out using a suction pump at 27 LHM and this constant flux was maintained throughout this investigation. However, the flux was increased to 29 LHM during days 297–303 owing to the breakage of membrane module during handling. The membrane module breakage has resulted from loosening of membrane module and it damaged the surface of membrane. This evidently increased the SS concentration in the effluent. The membrane adopted for the experiment is an assembly of multiple pieces of membranes, i.e. module, and every single piece has an individual valve. In this experiment, the pilot operated with a constant flow rate (Q). How-ever, during the process of finding the membrane breakage, indi-vidual modules were tested one by one by closing the valves. While closing the valves, the permeate flux has increased to a cer-tain extent. The air compressor was installed under the membrane module to scour the membrane fibers, and keep the DO above 2 mg/L in aerobic tank. Whereas, the DO in the anoxic tank was maintained below 0.3 mg/L. Sodium acetate was used as the source for supplementary carbon and the C/N ratio of the MBR system was varied from 1 to 9.3 by supplying sodium acetate under various flow rates. During days 1–19, MBR system was operated without supplementary carbon source. The various C/N ratios investigated in the present study, their time and the corresponding influent wastewater characteristics are shown inTable 2. The pH of the sys-tem was maintained between 7 and 7.5 by supplying sodium bicar-bonate. During days 1–102, the MLSS and MLVSS concentrations were around 6600 and 2600 mg/L, and increased to 8500 and 4200 mg/L, respectively, between days 127 and 232. Subsequently, the MLSS and MLVSS concentrations were increased rapidly to maximum of 16,000 and 9000 mg/L, respectively, when the C/N was increased to 9.3 during days 240–269. In the final stage (after day 276), the MLSS and MLVSS concentrations maintained at a sta-ble level, i.e. 11,000 and 6000 mg/L, respectively.

2.3. Quantification of bacteria by real-time PCR

As a first step, DNA was extracted using the FastDNA SPIN Kit for Soil (MP Biomedicals, Solon, OH, USA), in accordance with the manufacturer’s instructions. The concentrations of DNA were

Fig. 1. Schematic diagram of the MBR system.

Table 1

Characteristics of high-technology industrial wastewater.

Parameters Range Mean

mg/L SS 18–196 84 VSS 2–66 33 COD 36–108 64 BOD5 27–73 36 NHþ 4-N 45–85 63 NO 2-N 0–4 0.5 NO 3-N 0.5–18 7 TKN 48–124 68 TNa 47–94 71 a The sum of NHþ 4-N, NO3-N and NO2-N.

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determined with a NanoDrop ND-2000 spectrophotometer (Nanodrop Technologies, Wilmington, DE, USA). Subsequently, a LightCycler 2.0 system (Roche Diagnostics, Mannheim, Germany) was employed for the real-time PCR to quantify bacterial and arc-heal amoA, total Nitrospira and Nitrobacter and total bacterial 16S rRNA, and nirS genes.Table 3andTable 4show the primer infor-mation and real-time PCR conditions, respectively. The PCR reac-tion mixture (20

l

L) contained 10

l

L of 2  SYBRÒ Premix Ex

Taq™ (Perfect Real Time; TaKaRa Bio, Otsu, Japan), each primer and 20 ng of DNA extract. Melting curve analysis of the PCR prod-ucts was conducted following each real-time PCR to confirm that the fluorescence signal originated from specific PCR products and not from primer to dimers or other artifacts.

Quantitative PCR efficiency for all standard curves of the six genes was more than 1.89 and the R2value for all six standard

curves was more than 0.99. When converting copy number to cell number, assumed gene copy number/cell is 2 for bacterial amoA gene, 1 for archaeal amoA gene, 1 for Nitrospira 16S rDNA, 1 for Nitrobacter 16S rDNA, 1 for nirS gene, and 3.6 for bacterial 16S rDNA (Degrange and Bardin, 1995; Philippot, 2002).

2.4. Analytical methods

The concentrations of SS, VSS, COD, BOD, NHþ 4-N, NO

 2-N and

NO3-N in the wastewater were analyzed using the Standard

Meth-ods (APHA, 1999). The SS concentration was measured by drying the sample at 103–105 °C; and subsequently, the residue was ig-nited at 550 °C to calculate the VSS concentration. The COD was measured by open reflux method. The BOD of the system was mea-sured by the 5-day BOD test and the membrane electrode method was used to determine DO content in the samples. The NHþ

4-N,

NO

2-N and NO 

3-N concentrations were measured

spectrophoto-metrically using a UV spectrophotometer (Shimadzu, Japan). From the analytical data, nitrification rate was calculated from the ammonia removal rate. Similarly, denitrification percentage was workout from the amount of total nitrate removed in the system

(i.e. including the removal of nitrogen which produced from the oxidation of ammonium nitrogen).

Nitrification rate and denitrification percentage were calculated using the Eqs. (1) and (2), respectively. Denitrification percentage was defined as the nitrogen removed from oxidized ammonium nitrogen:

RNitrification¼ Qinð½NHþ4-Nin ½NH þ

4-NoutÞ=½VSSreactorVreactor ð1Þ

Denitrification ð%Þ ¼ fð½NHþ 4-Nin ½NH þ 4-NoutÞ  ½NO  3-Nout  ½NO3-NinÞ=ð½NH þ 4-Ninþ ½NO  3-Nin  ½NHþ4-NoutÞg  100% ð2Þ

3. Results and discussion 3.1. MBR pilot performance 3.1.1. TMP

The variation of TMP in the pilot scale MBR is shown inFig. 2. In the whole period, TMP was increased gradually with a constant flux. During days 1–120, TMP increased from 5.04 to 10.95 cm-Hg. Subse-quently, the TMP shoot-up to a level a 50 cm-Hg on day 121 owing to some operational problems and the first chemical cleaning was car-ried out and it proceeded for 3 days. After chemical cleaning, the TMP returned to the initial value, i.e. around 5 cm-Hg. In the follow-ing period, the TMP situation cycled as above.

3.1.2. Influent and effluent characteristics

The characteristics of the high-technology industrial wastewater used in the present study are shown inTable 1. The concentrations of SS, VSS, COD, BOD5, NHþ4-N, NO



2-N and NO 

3-N were 84, 33, 64, 36,

63, 0.5 and 7 mg/L, respectively. The BOD5=NHþ4-N ratio is around

0.6. The concentrations of NHþ4-N and TKN were almost similar, which

reveal that organic protein content in the wastewater is petite.

Table 2

Characteristics of influent, effluent and removal efficiencies at different C/N ratio. C/Na

Period (d) Influent characteristics, mg/L Effluent characteristics, mg/L (maximum removal efficiency) SS BOD5 COD NHþ4-N NO2-N NO3-N TN Supplementary BODL, kg/day SS BOD5 COD NHþ4-N NO2-N NO3-N TN

1 1–19 99 42 68 62 1 7 69 – 2 (100) <1 (100) 8 (91) 2 (100) N.D. 74 76 (11) 1.6 20–42 76 43 63 66 <1 7 74 0.55 <1 (100) <1 (100) 7 (93) 2 (100) N.D. 66 69 (26) 2.8 43–82 89 43 66 56 <1 9 65 1.20 <1 (100) <1 (100) 6 (97) 2 (100) N.D. 61 63 (24) 3.6 83–164 74 43 64 67 <1 7 74 2.13 <1 (100) <1 (100) 7 (96) 6 (100) <1 53 60 (44) 4.8 165–233 98 47 64 71 <1 6 77 4.30 <1 (100) <1 (100) 6 (98) 2 (100) N.D. 45 48 (67) 9.3 240–302 74 42 57 57 <1 8 68 6.52 1 (100) 1 (100) 7 (91) 3 (100) N.D. 10 13 (98) a

C/N ratio is based on the average value.

Table 3

Primers used in this study.

Target gene Primer Nucleotide sequence (50–30) References

Bacterial amoA gene amoA-1F GGGGTTTCTACTGGTGGT Rotthauwe et al. (1997) amoA-2R CCCCTCKGSAAAGCCTTCTTC

Archaeal amoA gene Arch-amoAF STAATGGTCTGGCTTAGACG Francis et al. (2005) Arch-amoAR GCGGCCATCCATCTGTATGT

Nitrospira 16S rRNA gene EUB338f ACTCCTACGGGAGGCAGC Regan et al. (2002) Ntspa0685 M CGGGAATTCCGCGCTC

Nitrobacter 16S rRNA gene EUB338f ACTCCTACGGGAGGCAGC Regan et al. (2002) NIT3 CCTGTGCTCCATGCTCCG

nirS gene cd3aF GTSAACGTSAAGGARACSGG Throback et al. (2004)

R3 cd GASTTCGGRTGSGTCTTGA

Bacterial 16S rRNA gene Eub338 ACTCCTACGGGAGGCAGCAG Fierer and Jackson (2005) Eub518 ATTACCGCGGCTGCTGG

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Table 2shows the characteristics of the influent and effluent, and the removal efficiencies of various parameters in each period. The SS concentration in the influent was above 70 mg/L under all periods and less than 1 mg/L was observed in the effluent and the corresponding removal efficiencies were around 100%. This is attributed to the removal of solids by the membrane pores (Lerner et al., 2007). The BOD5in the influent was around 44 mg/L. After

the treatment, the effluent concentration and removal efficiency were less than 1 mg/L and 100%, respectively, at C/N ratios below 4.8. The COD concentration of influent was around 65 mg/L and less than 8 mg/L in effluent under all the C/N ratios investigated, which shows the COD removal efficiency above 91%. The NHþ

4-N

concentration in the influent and effluent were around 63 and 3 mg/L, respectively, indicating 100% removal efficiency. The NO

2-N concentration in the influent was less than 1 mg/L and most

of the time the NO2-N concentration in the effluent was 0 mg/L,

indicating that all the NHþ

4-N in the influent was converted to

NO 2-N and subsequently to NO  3-N. The NO  3-N concentration in

the influent was less than 9 mg/L, and its effluent concentration was above 60 mg/L when the C/N ratio was below 3.6. However, the NO

3-N concentration decreased gradually while at higher

C/N ratios (>3.6). These results demonstrate that the variation of C/N ratio has no significant effect on the removal efficiencies of SS, BOD5, COD and NHþ4-N. Moreover, these observations reflect

that organic carbon and nitrification were highly successful irre-spective of the various C/N ratios adopted. However, the removal of NO

3-N in the MBR system, i.e. denitrification, was highly

depen-dent on the C/N ratio and it was successful only when the ratio is maintained above 3.6. The lowest NO3-N concentration observed

in the effluent was 10 mg/L at a C/N ratio 9.3.

3.2. Effect of C/N ratio on pollutant removal 3.2.1. Effect of C/N ratio on removal efficiencies

The sodium acetate as extra organic carbon source was used to vary the C/N ratio, and converted to BODLto determine the dosage.

The relationship between C/N ratio and the removal efficiencies of COD, BOD5, NHþ4-N and TN were illustrated inFig. 3. The COD,

BOD5, NHþ4-N removal efficiencies were stable and good, even the

C/N ratio was varied from 0.9 to 9.3. The experimental outcomes indicate that above 90% BOD5removal and above 80% for COD

re-moval could be achieved in the MBR system. Moreover, the NHþ 4-N

removal efficiency was higher than 80% throughout the experi-ment irrespective of the various C/N ratios adopted for the investi-gation. On contrary, a significant relationship between TN removal and C/N ratio was observed. The TN removal efficiency increased with the increase in C/N ratio, i.e. more than 60% TN removal effi-ciency was observed when the C/N ratio higher than 8. However, a maximum TN removal efficiency of 98% was achieved at a C/N ratio of 9.3. This result is in good agreement with the previous investi-gations (Tan and Ng, 2008).

3.2.2. Effect of C/N ratio on nitrification and denitrification

Fig. 4shows the variation of nitrification rate and denitrification percentage with different C/N ratios. The nitrification rate was relative high when the C/N ratio was less than 4. The highest denitrification rate of 0.59 g of N/g of VSS-d was observed at a C/ N ratio of 2.5. The nitrification rate was always below 0.2 g N/ g VSS d when the C/N ratio was greater than 5 ( Komorowska-Kauf-man et al., 2006). In general, the nitrification rate is expected to

Table 4

Real-time PCR conditions used in this study.

Target gene Primer conc. (lM) Hot start Cycle No. Denature Annealing Extension

Temp.(°C) Time (s) Temp. (°C) Time (s) Temp. (°C) Time (s) Temp. (°C) Time (s)

Bacterial amoA gene 0.2 95 20 50 95 7 55 20 72 20

Archaeal amoA gene 0.2 95 20 50 95 10 53 20 72 30

Nitrospira 16S rRNA gene 0.2 95 20 40 95 10 58 20 72 20

Nitrobacter 16S rRNA gene 0.1 95 20 40 95 7 60 20 72 40

nirS gene 1.0 95 10 30 95 5 57 20 72 15

Bacterial 16S rRNA gene 0.2 95 10 30 95 5 53 20 72 15

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decrease with the increase in the C/N ratio owing to the competi-tive growth of heterotrophic organisms in the system.

The experimental result also pointed out that denitrification was not significant when the C/N ratio was less than 3. However, it increased considerably when the C/N ratio was higher than 3. This could be due to the insufficiency of the organic source for the growth of heterotrophic denitrification. An average value of 83% denitrification was reached with C/N ratio above 8, and achieved completely at a C/N of 9.3.Carrera et al. (2004)reported complete denitrification at a C/N ratio of 7.1 in a pre-denitrification process. Fu et al. (2009a,b)obtained a complete denitrification

with C/N ratio of 9.3 in an A/O MBR. These results also support the present investigation.

3.3. Quantification of bacteria by real-time PCR

The quantification results show that the proportion of ammonia oxidizing bacteria to total bacteria in the high C/N ratio (C/N = 9.3) sludge is around 0.05%, which is 10 times lower than that in the low C/N ratio sludge (C/N = 0.9). It is suggested that the bountiful carbon source in the high C/N ratio sludge enriched the growth of heterotrophic microorganisms and then slightly inhibited the

Fig. 3. COD, BOD5, NHþ4-N and TN removal efficiencies with different C/N ratio in the MBR.

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growth of ammonia-oxidizing bacteria. Nitrospira is the major nitrite-oxidizing bacteria observed in both high and low C/N ratio sludge, and its magnitude was two orders higher than Nitrobacter. The nitrite concentration in the influent supplied to MBR was <1 mg/L throughout the experimental period which maintained a low nitrite condition. It is anticipated that under such a low nitrite condition, Nitrospira will be the predominant organisms in the MBR system. Since Nitrospira has high substrate affinity, which is useful for its predominance in the low nitrite environments (Schramm et al., 1999). However, no significant difference in denitrifier population was observed between high and low C/N ratio sludge samples.

4. Conclusions

The effect of supplementary carbon source in treating high-technology industrial WW by using MBR was investigated under various C/N ratios. The removal efficiencies of SS, COD and BOD5

were not affected by the change in C/N ratio. Almost complete SS and BOD5 removal efficiencies were observed throughout the

experimental period, and above 80% COD removal efficiency was observed under all the C/N ratios investigated. However, the TN removal efficiency increased with the increase in C/N ratio and a maximum of 98% TN removal was obtained at a C/N of 8.1. Nitrification rate decreased with the increase in C/N ratio and a highest rate of 0.59 g of N/g of VSS d was obtained at a C/N of 2.5, and decreased quickly while C/N ratio greater than 5. On the other hand, the denitrification percentage increased with the in-crease in C/N ratio and a complete denitrification (no nitrate re-mained in effluent) was observed when the system C/N ratio was maintained at 9.4. In addition, ammonia oxidizing bacteria to total bacteria under low C/N ratio condition is 10 times higher than that observed in the high C/N ratio condition. The whole experimental results reveal that a C/N ratio of 8 and above is most appropriate for the occurrence of effective simultaneous nitrification and denitrification.

Acknowledgements

This research was funded by AXLON International Engineering Corporation. We would like to express our gratitude for staves of AXLON for assisting in the pilot scale MBR work and also for solving the technical issues in MBR plant operation during the course of this work. We also thank Century Environtech Co. Ltd. and AquaLab Co. Ltd. for providing the membrane modules.

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數據

Fig. 1. Schematic diagram of the MBR system.
Table 2 shows the characteristics of the influent and effluent, and the removal efficiencies of various parameters in each period
Fig. 3. COD, BOD 5 , NH þ 4 -N and TN removal efficiencies with different C/N ratio in the MBR.

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Breu and Kirk- patrick [35] (see [4]) improved this by giving O(nm 2 )-time algorithms for the domination and the total domination problems and an O(n 2.376 )-time algorithm for

A subgroup N which is open in the norm topology by Theorem 3.1.3 is a group of norms N L/K L ∗ of a finite abelian extension L/K.. Then N is open in the norm topology if and only if

The Liouville CFT on C g,n describes the UV region of the gauge theory, and the Seiberg-Witten (Gaiotto) curve C SW is obtained as a ramified double cover of C g,n ... ...

Generalized LSMA theorem: The low-energy states in gapped phases of SU (N ) spin systems cannot be triv- ially gapped in the thermodynamical limit if the total number of

Q: Can we at least find the exact string theory background that gives our universe. A: A

Total energies and Cartesian coordinates for the lowest singlet and triplet states of n-acenes (n = 2 to 46) by spin-unrestricted TAO-LDA (θ = 7 mHartree)/6-31G ∗ (S3 to S88)..