ARTICLE IN PRESS

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Water Research 39 (2005) 4941–4952

www.elsevier.com/locate/watres

Evaluation of kinetic parameters of a sulfur–limestoneautotrophic denitrification biofilm process

Hui Zenga, Tian C. Zhangb,�

a208 Cupples II, Department of Environmental Engineering Science, Washington University, St. Louis, MO 63130, USAb205D PKI, Civil Engineering Department, University of Nebraska-Lincoln at Omaha Campus, Omaha, NE 68182-0178, USA

Received 21 February 2005; received in revised form 17 September 2005; accepted 24 September 2005

Abstract

In this study, four kinetic parameters of autotrophic denitrifiers in fixed-bed sulfur–limestone autotrophic denitrification

(SLAD) columns were evaluated. The curve-matching method was used by conducting 22 non-steady-state tests for

estimation of half-velocity constant, Ks and maximum specific substrate utilization rate, k. To estimate the bacteria yield

coefficient, Y and the decay coefficient, kd, two short term batch tests (before and after the starvation of the autotrophic

denitrifiers) were conducted using a fixed-bed SLAD column where the biofilm was fully penetrated by nitrate-N. It was

found that Ks ¼ 0.398mg NO3�–N/l, k ¼ 0.15d�1, kd ¼ 0.09–0.12d�1, and Y ¼ 0.85–1.11g VSS/g NO3

�–N. Our results are

consistent with those obtained from SLAD biofilm processes, but different from those obtained from suspended-growth

systems with thiosulfate or sulfur powders as the S source. The method developed in this study might be useful for

estimation of four Monod-type kinetic parameters in other biofilm processes. However, cautions must be given when the

estimated parameters are used because the measurements of the biomass and the biofilm thickness could be further

improved, and the assumption of sulfur being a non-limiting substrate needs to be proved.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Autotrophic denitrification; Kinetics; Sulfur; Nitrate; Biofilm

1. Introduction

The sulfur–limestone autotrophic denitrification

(SLAD) process for treatment of nitrate contaminated

water has been studied for decades. In the past, most of

fundamental studies (e.g., kinetics) about the SLAD

process were conducted by using suspended-growth

systems with nitrate or nitrite as the substrate (the

electron acceptor) and thiosulfate (S2O32�) or sulfur

powders (50–100mm in diameter), instead of sulfur

stones, being the S source (the electron donor)

e front matter r 2005 Elsevier Ltd. All rights reserve

atres.2005.09.034

ing author. Tel.: +1402 554 3784;

3288.

ess: tzhang@unomaha.edu (T.C. Zhang).

(Batchelor and Lawrence, 1978; Justin and Kelly,

1978; Claus and Kutzner, 1985; Hashimoto et al.,

1987). This is due to the difficulty in completely mixing

sulfur stones (such as sulfur powders or particles) with

other components to make a reactor work properly.

The SLAD process was believed to follow Monod

equations within the biofilm. If the nitrate concentration

was relatively low, however, it showed first-order

kinetics in bulk solution (Sikora and Keeney, 1976). In

a slurry reactor (Batchelor and Lawrence, 1978), when

the nitrate concentration in the SLAD system was high

enough to penetrate the whole biofilm, the denitrifica-

tion rate followed a zero-order reaction in bulk solution.

Otherwise, the denitrification rate followed a half-order

reaction in the bulk solution (Batchelor and Lawrence,

d.

ARTICLE IN PRESS

Nomenclature

a specific area of sulfur and limestone, 1/L

A reactor cross-sectional area, L2

b overall biofilm-loss coefficient, 1/T

bdet specific biofilm-detachment loss coefficient,

1/T

D molecular diffusivity of nitrate in bulk

solution, L2/T

Df molecular diffusivity of nitrate in biofilm

(assuming Df ¼ 0.8 D), L2/T

dp diameter of sulfur particle, L

HRT empty-bed hydraulic retention time, T

J substrate flux into biofilm, M/L2T

Jexp substrate flux into biofilm calculated based

on test results, M/L2T

k maximum specific substrate utilization rate,

1/T

kd bacteria decay coefficient, 1/T

Ks half-velocity constant, M/L3

L thickness of the effective diffusion layer, L

Lf biofilm thickness, L

Mb total biomass in biofilm as VSS, M

Q the feed flow rate, L3/T

Qr the recycle flow rate, L3/T

r substrate utilization rate, M/L3T

r0, rd substrate utilization rate without or after

starving, respectively, M/L3T

Rem Reynolds number of the media

Savg, So, Se the logarithm average, feed, and effluent

concentration of nitrate-N, respectively, M/

L3

Sb substrate concentration in bulk liquid, M/L3

Sc Schmidt number, m/rD

Sf substrate concentration at that point in the

film, M/L3

Sin actual substrate concentration at inlet of

reactor, M/L3

Smin minimum substrate concentration for sus-

taining biomass growth, M/L3

Ss substrate concentration at interface of bio-

film and bulk liquid, M/L3

Sw substrate concentration at the surface of

attachment, M/L3

td starving time, T

v superficial flow velocity, L/T

V volume of sulfur and limestone packed, L3

Xf biomass density in biofilm (i.e., biomass per

biofilm volume), M/L3

Y bacteria yield coefficient

e porosity of media

Z biofilm effectiveness factor

m absolute viscosity of liquid, M/LT

mm maximum specific growth rate, 1/T

r liquid density, M/L3

t biofilm depth dimension, [KsDf/(kXf)]1/2, L

Fp, Fm, Cs parameters related with Z.

H. Zeng, T.C. Zhang / Water Research 39 (2005) 4941–49524942

1978). In both cases, the nitrate uptake rate in biofilm

was assumed to follow zero-order kinetics. These results

(Batchelor and Lawrence, 1978) were confirmed in other

studies where the SLAD process was used for nitrate

removal in groundwater and septic tank wastewater

(Liu, 1992; Koenig and Liu, 2001; Zhang, 2003). While

the results obtained from these suspended-growth

systems are informative, sufficient information on

Monod-based kinetics of a SLAD biofilm process is

still not available. Without these parameters, it is

difficult to model, design or evaluate a SLAD biofilm

system (Le Cloirec, 1985), or compare the system with

other denitrification technologies. It was toward this

objective that the present study was directed to develop

methods to experimentally evaluate the four Monod-

type kinetic parameters in a SLAD biofilm process.

2. Materials and methods

2.1. Fixed-bed columns and culture conditions

Column reactors were used to conduct the kinetic

study (Fig. 1 and Table 1). The columns were partially

filled with granular elemental sulfur (diame-

ter ¼ 2.38–4.76mm, Georgia Gulf Sulfur, Bainbridge,

GA) and limestone at a ratio of 2:1 (Liu and Koenig,

2002). A peristaltic pump (Cole-Parmer, IL, USA) with

two different standard pump heads (Model 7013-20 and

Model 7018-20) was used to provide constant influent

and recycle flow into the reactor. The high recycle ratio

(39.6) kept the column as a completely-stirred tank

reactor (CSTR). The feed solution was artificial ground-

water (Table 2) with various nitrate-N (made from

KNO3, Mallinckrodt Co., Kentucky, USA) concentra-

tions (Claus and Kutzner, 1985) and trace nutrients that

were made by dissolving a tablet of Centrum (Wyeth

Consumer Healthcare, Madison, NJ, USA) into 500ml

tap water. Before use, each new tank of the feed solution

was bubbled with N2 gas for 30min to remove dissolved

oxygen. The N2 gas was bubbled very gentle (i.e., 2

bubbles per second) during the test period; extra N2 gas

could escape from the vent of the feed tank (Fig. 1).

After being inoculated with seed sludge (Zhang,

2002), the columns were fed with 30mg NO3–N/l at an

empty-bed hydraulic retention time, HRT of 3.56 h; the

corresponding steady state condition was designated as

basic steady state conditions 1 (BSSC1). We assumed

BSSC1 was reached (usually took 43–4 weeks) if (1) the

ARTICLE IN PRESSH. Zeng, T.C. Zhang / Water Research 39 (2005) 4941–4952 4943

differences in effluent concentrations (e.g., NO3–N)

from 3 continuous daily tests were o5% of average

values, (2) the sign of biofilm growth and gas bubbles

attached on the media surfaces were obvious, and (3) gas

was collected constantly.

2

Qout

Qr

Qin

1

N2

S/L Bed

Feed Tank

Water Seal

Gas Outlet

Drainage Column Pumps

Qr+QinInlet

Venting

Water Seal

Fig. 1. Experimental set-up for kinetics studies. Note: 1 and 2

are sampling ports; Qin, Qout, and Qr ¼ flow rate of influent,

effluent and recirculation, respectively.

Table 1

Characteristics of SLAD reactors used for kinetics study

Characteristics Reactors

Study Ks and k

Length of media and reactor, (cm) 5.7 and 19.0

Diameter of reactor (cm) 3.81

Working volume (mediaþporosity) (S/L) (cm3) 65.10

Cross-sectional area of reactor, A (cm2) 11.40aDiameter of particles (cm) 0.246

Specific area of particle, a (1/cm) 13.90

Influent flow rate (cm3/min) 0.3048

Porosity, e 0.43

Recycle ratio, Qr/Qin 39.7

Superficial liquid velocity [(QþQr)/A] (cm/d) 1567.00

Liquid density (mg/cm3) 998.2

Viscosity (mg/h-cm) 36072

Df (cm2/h) 0.03744

D (m2/h) 0.0468

Empty-bed hydraulic retention time (Q/V) (h) 3.56

Lf (cm) 0.0084�0.0060

Biomass, mg VSS/ml media+porosity volume 1.62

Biofilm density, Xf, mg/cm3 of biofilm volume 13.87

NO3–N in feedc (mg/l) 30

adp is geometric mean of 2.38 and 4.76mm, shape factor ¼ 0.73 (MbSuperficial liquid velocity here ¼ Qr/A, the one during starving pecThis is the nitrate-N concentration in feed at the BSSC1 and BSSC

would be in a range of 0.4–1200mg/l (see Table 2 below).

2.2. Estimation of K s and k

Non-steady state tests. After the reactor (fed with

30mg NO3–N mg/l substrate) reached the BSSC1, 22

short-term tests were consequently conducted by feeding

the reactor with artificial groundwater containing

0.4–1200mg/l NO3–N (Table 2). The trace nutrient

was the same as in culture conditions. For each run, the

feed solution was bubbled with nitrogen gas. The reactor

was first drained off and then washed three times with a

new feed solution. After that, the reactor was loaded

with the new feed solution and started running. After

running 7 h, 5 samples were collected. Upon completion

of each test, the reactor was allowed to return to the

original situation (i.e., 30mg NO3–N/l in feed and an

HRT ¼ 3.56 h) and kept running until the BSSC1 was

achieved. The next run was conducted in the same way.

Theory and procedure for estimation of Ks and k. When

a biofilm is at steady state, the biomass per unit surface

area is constant in time, although the biomass at any

point is not at steady state. This means that an increase

in biomass due to substrate utilization is balanced by the

loss from intrinsic decay and external detachment

(Rittmann and McCarty, 2001). The real thickness of

biofilm may keep increasing but the active thickness may

Study kd and Y Measure biomass of 30mg

NO3–N/l

6.9 and 34.0 5.9 and 19.0

3.81 3.81

78.63 67.26

11.40 11.40

0.246 0.246

13.90 13.90

0.307 0.32

0.43 0.43

39.08 39.21b1515.48 1625.33

998.2 998.2

36072 36072

0.03744 0.03744

0.0468 0.0468

4.27 3.50

0.0041�0.0019 0.0084�0.0060

1.34 1.62

23.51 13.87

5 30

etcalf and Eddy, 2003).

riod with no inflow.

2. For non-steady-state runs, the nitrate-N concentration in feed

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Table 2

Feed solution compositiona

Component Concentration (mg/l) Component Concentration (mg/l)

NO3�–N 0.4–1200 Phosphate (ortho) 0.3

Alkalinity 300 Sulfate 150

Fluoride 0.25 pH 7.8–8.5

Iron 0.3

aFeed solution made with tap water. Nutrient is added as 1ml per liter of feed solution.

H. Zeng, T.C. Zhang / Water Research 39 (2005) 4941–49524944

keep the same so that the performance of substrate

utilization of biofilm is at steady state (Skowlund, 1990;

Rittmann and McCarty, 2001). If a sudden change in

substrate occurs, although the solution phase steady

state can be achieved very quickly (e.g., within hours),

the biofilm properties were not at steady state. There-

fore, the test during a short period of time is at non-

steady state. In a SLAD biofilm, for a short period (e.g.,

several hours) the biofilm responses to a sudden change

in substrate (e.g., the loading rate or concentration) still

are based on the original biomass since autotrophic

denitrifiers grow slowly. Therefore, we can assume the

biofilm thickness to be constant. In a non-steady state

biofilm at any given biofilm thickness (Lf), the relation-

ship between the flux into the biofilm (J) and the

substrate concentration in the interface of the biofilm

and the diffusion layer (Ss) could be solved, for a short

period, from the pseudo analytical solution (Atkinson

and Davies, 1974; Rittmann and McCarty, 2001). Based

on this pseudo analytical solution, the intrinsic Ks and k

can be estimated from the non-steady-state experimental

results using a family of standard curves that has only

three variables (denoted by an asterisk).

J� ¼ Jt=ðK sDÞ, (1)

S�s ¼ Ss=Ks, (2)

L�f ¼ Lf=t, (3)

where J* ¼ the dimensionless substrate flux into the

biofilm; J ¼ the substrate flux into the biofilm, M/L2 T.

t ¼ biofilm depth dimension, [KsDf/(kXf)]1/2, L; Ss

*¼ di-

mensionless substrate concentration in the interface of

the biofilm and diffusion layer; Lf*¼ the dimensionless

biofilm thickness. Ks ¼ half-velocity constant, M/L3;

k ¼ maximum specific substrate utilization rate, 1/T;

Lf ¼ the biofilm thickness, L; Xf ¼ the biomass density

in biofilm (i.e., biomass per biofilm volume), M/L3; Ss

and Sb ¼ substrate concentration in the interface of the

biofilm and diffusion layer and in bulk liquid, respec-

tively, M/L3; and D and Df ¼ the molecular diffusivity

of nitrate in bulk solution and in biofilm (assuming

Df ¼ 0.8 D), respectively, L2/T.

The family of curves (Fig. 2a) was generated with

Excel software that calculated J* values for a wide range

of Ss* and Lf

* using solutions presented in previous

studies (Atkinson and Davies, 1974; Rittmann and

McCarty, 2001) for simultaneous reaction with diffusion

within a biofilm. An overlay transparency was made

from Fig. 2a. The following steps were followed to

estimate Ks and k (Rittmann et al., 1986):

(1)

Plot Fig. 2b with log Jexp (calculated based on test

results) vs. log Ss for each run (data shown in Table

3) on a separate graph having the same scale as the

overlay (Fig. 2a).

(2)

Manipulate the overlay (Fig. 2a) over the data plot

(Fig. 2b) until the experiment points fit a single

overlay curve.

(3)

Find the point on experimental Ss axis that lines up

with the overlay value Ss*¼ 1, this Ss ¼ Ks.

(4)

At the point where the Ss*¼ 1 line intersects the Lf

*

curve chosen to fit the data, read the log J* and log

Jexp.

(5)

Calculate k from the values obtained in step 4:

k ¼ ðJexp=J�Þ22Df=ðKsX fD2Þ. (4)

(6)

Check if Lf* is consistent with the experimental Lf,

L�f ¼ Lf=½2K sDf=ðkX f Þ�1=2 (5)

(7)

Repeat step 2 to 6 if Lf* is not with experimental Lf

until they are consistent.

Reactor used for biomass measurement. In this study,

non-steady-state tests for Ks and k estimation were run

right after the reactor reached the BSSC1 (i.e., at 30mg

NO3–N/l in feed and an HRT ¼ 3.56 h), which did not

allow us to destroy the biofilm for biomass and its

thickness measurements. After running for two months,

biomass accumulated on the surface of the sulfur stones.

Since a large part of the biomass might be non-active,

the biofilm was not suitable for measurements of the

biofilm thickness and biomass density. Therefore, the

CSTR was backwashed after all non-steady-state tests

had been completed; it then was set up and run again in

ARTICLE IN PRESS

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

-3 -2 -1

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

-5 -4 -3 -2 -1 2

(b)

Lf* = 100

Lf* = 0.001

Log

J*

Log Ss*(a)

Log Ss

0 1 2 3 4

0 1

Log

Jex

p

Fig. 2. (a) Family of dimensionless curves. From bottom to top

Lf* is 0.001, 0.0016, 0.0025, 0.0040, 0.0064; 0.01, 0.016, 0.025,

0.04, 0.064; 0.10, 0.16, 0.25, 0.40, 0.64; 1.0, 1.6, 2.5, 4.0, 6.4; 10,

16, 25, 40, 64, and 100, respectively; the thick black curve

Lf� ¼ 1. (b) Results of non-steady-state tests.

H. Zeng, T.C. Zhang / Water Research 39 (2005) 4941–4952 4945

the exact same manner as the one used for Ks and k

estimation to measure the biofilm thickness and biomass

once it reached the BSSC1.

2.3. Estimation of Kd and Y

Batch tests for Kd and Y estimation. A column reactor

(Table 1) was set up, inoculated and cultured in the same

way as the one used for Ks and k estimation except that

it was fed with 5mg/l NO3–N at an HRT of 4.27 h when

pumping was started (Tables 1 and 2). After it reached

the steady state condition (designated as BSSC2 for a

feed of 5mg/l NO3–N at an HRT of 4.27 h), the reactor

was drained off and rinsed with 50mg/l NO3–N feed

solution several times before use. Then 200ml substrate

(same as Table 2) with 50mg/l NO3–N was quickly

injected into the batch reactor. The reactor stopped

receiving its continuous feed but kept its recycle running

with the same recycle flow so that it was run as a

completely mixed batch reactor. Samples of 2-ml volume

each were collected about every 30min for 4 h. After this

short-term test the column was then brought back to the

CSTR mode with 5mg/l NO3–N in the feed. When the

column reached the BSSC2 again, it was starved for

30 h. During the starving period, feed solution without

nitrate but with the same other components as shown in

Table 2 was fed continuously at a flow rate of 0.307 cm3/

min (HRT ¼ 4.27 h, and at the same recycle ratio). After

starving, another 4-h batch test was conducted using the

same procedure and substrate (50mg/l NO3–N).

Measurements of the biofilm thickness and biomass

density were made before any experiment for estimation

of kd was conducted. Two similar column reactors with

the same HRT of 4.27–4.3 h were fed with 5mg/l

NO3–N and kept running until the BSSC2 was reached.

Then the sulfur and limestone particles were taken out

for biomass measurements. Then the sulfur and lime-

stone particles were backwashed. The reactors were

filled back and used to conduct the experiments for

estimation of kd.

Theory and procedures for estimation of kd and Y. At

any position within a fully-penetrated biofilm (Suidan et

al., 1987), substrate is utilized as

r ¼ � kX fSf=ðK s þ Sf Þ ¼ �kX fSs=ðK s þ SsÞ

¼ �kX fSw=ðKs þ SwÞ, ð6Þ

where r ¼ substrate utilization rate, M/L3T; Ks ¼ half-

velocity constant, M/L3; k ¼ maximum specific sub-

strate utilization rate, 1/T; Xf ¼ the biomass density in

biofilm, M/L3; Ss, Sf, and Sw ¼ substrate concentration

in the interface of the biofilm and diffusion layer, at any

point in the biofilm, and at the surface of attachment,

respectively, M/L3. Integrating Eq. (6) over the biofilm,

ravg ¼ � ð1=Lf Þ

Z Lf

0

½kX fSs=ðKs þ SsÞ�dz

¼ � kX fSs=ðKs þ SsÞ, ð7Þ

where Lf ¼ the biofilm thickness, L; ravg ¼ the average

substrate utilization rate over the biofilm. If SsbKs, the

ARTICLE IN PRESS

Table 3

Results and calculated flux for short-term non-steady-state experiments

Sample set So (NO3–N) (mg/cm3) Se (mg/cm3) Sin (mg/cm3) Savg (mg/cm3) Jexp (mg/cm2-h) Ss (mg/cm3) Log Jexp Log Ss

1 0.0025 0.0002 0.000229 0.000199 0.00004654 0.000184 �4.3322 �3.7345

2 0.0156 0.0056 0.005806 0.005682 0.00020229 0.005618 �3.6940 �2.2504

3 0.0459 0.0274 0.027817 0.027588 0.00037527 0.027469 �3.4257 �1.5612

4 0.0597 0.0332 0.033803 0.033476 0.00053674 0.033306 �3.2702 �1.4775

5 0.0866 0.0641 0.064624 0.064347 0.00045530 0.064203 �3.3417 �1.1924

6 0.1256 0.0966 0.097327 0.096970 0.00058616 0.096785 �3.2320 �1.0142

7 0.0010 0.0000 0.000054 0.000041 0.00001960 0.000035 �4.7077 �4.4611

8 0.0476 0.0270 0.027507 0.027253 0.00041629 0.027121 �3.3806 �1.5667

9 0.0280 0.0067 0.007238 0.006973 0.00042993 0.006838 �3.3666 �2.1651

10 0.0280 0.0082 0.008726 0.008481 0.00039912 0.008355 �3.3989 �2.0781

11 0.0388 0.0164 0.016981 0.016704 0.00045247 0.016561 �3.3444 �1.7809

12 0.0172 0.0027 0.003035 0.002853 0.00029347 0.002760 �3.5324 �2.5591

13 0.0081 0.0005 0.000674 0.000576 0.00015281 0.000528 �3.8159 �3.2772

14 0.0124 0.0014 0.001697 0.001558 0.00022195 0.001488 �3.6537 �2.8274

15 0.0040 0.0002 0.000282 0.000231 0.00007776 0.000207 �4.1092 �3.6850

16 0.0020 0.0001 0.000133 0.000108 0.00003868 0.000096 �4.4125 �4.0195

17 0.0004 0.0000 0.000025 0.000019 0.00000804 0.000017 �5.0946 �4.7709

18 0.1707 0.1412 0.141876 0.141512 0.00059615 0.141324 �3.2246 �0.8498

19 0.2337 0.2092 0.209804 0.209502 0.00049591 0.209345 �3.3046 �0.6791

20 0.4159 0.3972 0.397690 0.397460 0.00037790 0.397341 �3.4226 �0.4008

21 0.5207 0.4857 0.486560 0.486130 0.00070669 0.485907 �3.1508 �0.3134

22 1.1773 1.1528 1.153403 1.153101 0.00049511 1.152945 �3.3053 0.0618

H. Zeng, T.C. Zhang / Water Research 39 (2005) 4941–49524946

term Ss/(Ks+Ss)E1, then

ravg ¼ �kX f . (8)

It should be pointed out that, in the experiment, a

high Ss could be obtained by keeping a high Sb in the

reactor because in this case the diffusion layer only made

a very small concentration gradient. In this study, we

used the following method to estimate the decay rate

coefficient, kd of the SLAD system with a fully-

penetrated biofilm and SsbKs (but not being high

enough to inhibit the denitrification).

(1)

The column was run (called reference run) as a batch

reactor that contained the same substrate as shown

in Table 2 plus an initial nitrate-N concentration of

50mg NO3–N/l. An average nitrate-N utilization

rate without starving, ro, of the reference run is

ro ¼ �kX f . (9)

(2)

The biofilm was then left without nitrate-N for a

sufficient time period, td (30 h in this study), to allow

decay to occur within the biofilm. The overall

biofilm loss comes from intrinsic decay of respiration

and mechanical detachment. Assuming the overall

biofilm loss coefficient (b, 1/T) follows the first-

order kinetics (Lesouef et al., 1992; Rittmann and

McCarty, 2001) and can be averaged across

the biofilm,

dX

dt¼ �bX f , (10)

where b ¼ overall biofilm-loss coefficient, 1/T; and

td ¼ starving time, T. Then, after td,

X f new ¼ X f expð�btdÞ: (11)

(3)

After the starving period, the column was run again

as a batch reactor at the same operation condition as

in the reference run. Another average nitrate-N

utilization rate after starving, rd, was measured as

rd ¼ �kX f expð�btdÞ: (12)

The overall biofilm loss coefficient was then calculated

by combining Eqs. (9) and (12):

b ¼ lnðro=rdÞ=td. (13)

Then the decay rate coefficient (kd) could be calculated

from Eq. (14):

kd ¼ b� bdet. (14)

The specific-detachment loss coefficient (bdet, 1/d) was

calculated by Eqs. (15) and (16), which were developed

by Rittmann for biofilm (Lf430mm) on smooth surfaces

ARTICLE IN PRESSH. Zeng, T.C. Zhang / Water Research 39 (2005) 4941–4952 4947

of fixed-bed porous media (Rittmann and McCarty,

2001).

bdet ¼ 8:42� 10�2s

1þ 433:2ðLf � 0:003Þ

� �0:58

, (15)

s ¼200umð1� eÞ2

d2pe3að7:46� 109Þ

, (16)

where e ¼ bed porosity; u ¼ superficial liquid velocity,

cm/d; m ¼ absolute viscosity, g/cm-d; a ¼ specific sur-

face area of the biofilm carrier, 1/cm; s ¼ shear stress, g/

cm-s2. It should be pointed out that when surfaces are

not smooth, biofilms tend to accumulate first in crevices

that are protected from shear stress; in theses cases, bdetapproaches zero, as long as the biofilms remain only in

the protected crevices. However, once the biofilms

emerge from the crevices and ‘‘smooth out’’ the surface

(which, by assumption, was the case in our SLAD

columns), detachment rates approach those of smooth

surface (Rittmann and McCarty, 2001), and thus, Eqs.

(15) and (16) are still valid.

Y can be calculated from b ( ¼ kd+bdet) by employing

a biomass balance on biofilm under steady-state condi-

tions (Rittmann and McCarty, 2001):

Y ¼ X fLfb=J. (17)

In this study, we used the effective factor Z to evaluate

whether the biofilm was fully-penetrated or not (Atkin-

son and Davies, 1974):

Z ¼ 1�tanhðfmÞ

fm

fFp= tanhðFpÞ � 1g

for Fpp1 or ð18Þ

Z ¼1

fp

�tanhðfmÞ

fm

f1= tanhðFpÞ � 1g for FpX1, (19)

where Fp ¼ FmCs[2(1+Cs)2(Cs�ln(1+Cs))]

�1/2; Fm ¼

[kXfLf2/KsDf]

1/2; Cs ¼ Sb/Ks. Ks ¼ half-velocity constant,

M/L3; k ¼ maximum specific substrate utilization rate,

1/T; Lf ¼ the biofilm thickness, L; Xf ¼ the biomass

density in biofilm, M/L3; Sb ¼ substrate concentration

in bulk liquid, M/L3; D, and Df ¼ the molecular

diffusivity of nitrate in bulk solution and in biofilm

(assuming Df ¼ 0.8 D), respectively, L2/T. In this study,

the biofilm was considered as fully-penetrated if ZE1.

2.4. Analytical methods

The column tests and all analyses were conducted at

room temperature (2471 1C). Nitrate, nitrite and sulfate

were analyzed by a Dionex DX 500 HPLC/IC (high

performance liquid chromatography/ion chromatogra-

phy) system (Dionex Co., Sunnyvale, CA) as per

methods previously reported (Zhang, 2002). The detec-

tion limits of the analytical methods for nitrate, nitrite,

and sulfate are 0.1mg/l. The analyses of replicate

samples range within73% of the mean value. All the

data reported in this paper was the average of the

measurements of at least two samples unless otherwise

specified. pH and DO were measured with previous

methods (Flere and Zhang, 1999; Zhang, 2002).

We assume that limestone does not provide surface

areas for growth of autotrophic denitrifiers but still

affects the biomass distribution in the media. To analyze

volatile suspended solids (VSS), 6 samples of about 2ml

(10–20 particles) sulfur and limestone particles were

taken out of the packing media throughout the column.

The particles were rinsed with deionized water repeat-

edly until no biomass could be observed by eyesight

(Flere and Zhang, 1999). The VSS of the washed-out

biomass was then analyzed as per Standard Method

(APHA et al., 1998). Biofilm thickness (Lf) was

measured with a microscope (Leitz Wetzlar, Germany).

The sample sulfur particle was placed on the glass slide

and then added with one drop of deionized water. Under

the microscope, the biofilm could be observed at the

edge of the particle surface. Since the biofilm has a

looser structure than the sulfur stone does, the

interfacial surface of the particle and the biofilm could

also be distinguished. For each sulfur stone, its biofilm

thickness was measured at three locations. Each time

over 20 particles were used for the average Lf

(n ¼ 20� 3). Biomass density (Xf) was calculated with

an equation: Xf ¼Mb/(LfVa), where Mb ¼ total biofilm

biomass as VSS in the media, M; V ¼ volume of the

media, L3; a ¼ specific area of the media, 1/L. Notice

that Xf has a units of mg VSS per ml biofilm (including

both water and biomass).

3. Results

3.1. General performance of SLAD columns

It took about one month for the SLAD columns to

reach the BSSC1. In all tests, the pH in influent and

effluent was 7.8–8.5 and 6.7–8.0, respectively, indicating

that limestone would supply sufficient alkalinity at the

2:1 ratio of sulfur to limestone. The effluent always

showed normal color of drinking water (i.e., no color).

No odor of sulfide was observed during the normal

operational time; no precipitate was observed in the

effluent. The influent and effluent TOC was between

3.0–5.0 and 4.0–9.0mg/l, respectively. The effluent

biomass was always very low (o10mg TSS/l and

1.0mg VSS/l). The production rate of sulfate was found

to be 7.10mg SO42� per mg NO3–N reduced. This data,

together with the gas (presumably nitrogen) production

rate indicates that the denitrification reaction was

ARTICLE IN PRESS

Table 4

Estimation of Ks and k

Lf* logSs log J* log Jexp Ks (mg/ml) k (1/h) Lf

*’(checked)

0.5 �3.4 �0.6 �3.6 0.000398 0.00619 0.45

Table 5

Effectiveness factors of biofilms used for kd and Y estimation

Ks (mg/l) Lf (cm) Xf (mg/l) De (cm2/h) k (1/h) S (mg/l) S/Ks Fm Fp Z

a0.398 0.0041 23510 0.03744 a0.0062 50 125.628 0.16139 0.01030 0.99996a0.398 0.0041 23510 0.03744 a0.0062 40 100.503 0.16139 0.01154 0.99996b0.045 0.0041 23510 0.03744 b0.176 50 1111.11 0.28914 0.006147 0.99999b0.045 0.0041 23510 0.03744 b0.176 40 888.889 0.28914 0.006876 0.99998

aKs and k were obtained from the values estimated in this paper.bKs and k were obtained from Claus and Kutzner (1985).

H. Zeng, T.C. Zhang / Water Research 39 (2005) 4941–49524948

completed with nitrogen formation following the stoi-

chiometry of the reaction (Batchelor and Lawrence,

1978). The DO values of influent were kept lower than

0.1mg/l after nitrogen gas bubbling. The DO values of

column reactors were measured after all experiments

were done and the reactors were opened. The DO value

of the one used for Ks and k was measured at 0.4mg/l

while that of the one used for kd and Y was measured at

0.9mg/l.

3.2. Estimation of K s and k

The experimental results of the 22 short-term tests are

shown in Table 3. The following equations were used to

calculate Ss and Jexp:

Savg ¼ ðSin � SeÞ= lnðSin=SeÞ, (20)

Sin ¼ ðQSo þQrSeÞ=ðQþQrÞ, (21)

Jexp ¼ ðSo � SeÞ=ðHRTaÞ, (22)

Ss ¼ Savg � LJexp=D, (23)

L ¼ DðRemÞ0:75ðScÞ2=3=ð5:7vÞ, (24)

Rem ¼ ½2rdp=ð1� eÞm�, (25)

where Savg, So, Sin, Se ¼ the logarithm average, feed,

actual inlet, and effluent concentration of nitrate-N,

respectively, M/L3; Q ¼ the feed flow rate, L3/T;

Qr ¼ the recycle flow rate, L3/T; L ¼ the thickness of

the effective diffusion layer, L, which is determined by

the empirical formula for porous media (Rittmann et al.,

1986); Rem ¼ Reynolds number of the media; r ¼ liquid

density, M/L3; dp ¼ diameter of the sulfur particle, L;

v ¼ the superficial flow velocity, L/T; e ¼ porosity of the

media; m ¼ absolute viscosity of liquid, M/LT, Sc ¼

Schmidt number, m/rD.

Log Jexp vs. log Ss in Table 3 was plotted in Fig. 2b.

Table 1 shows the conditions of the reactors at BSSC1

and BSSC2. Table 4 shows the estimation and the check

of Ks and k (Rittmann et al., 1986). The estimated

Ks ¼ 0.398mg/l NO3–N, and k ¼ 0.15 g NO3�–N/g

VSS-d.

3.3. Estimation of kd and Y

The biofilm thickness and biomass density were

measured at BSSC2 (i.e., the feed solution being 5mg/l

NO3–N and an HRT of 4.27 h). Table 5 lists the

corresponding effectiveness factors for the short-term

batch tests. Both the Ks and k values estimated in this

study and reported before (Claus and Kutzner, 1985)

were used to estimate the effectiveness factors. As shown

in Table 5, the effectiveness factors are all very close to 1

no matter which set of the kinetic parameters is chosen.

This, therefore, confirms that the biofilm was fully-

penetrated during our tests.

As shown in Fig. 3, the two slopes are the average

substrate utilization rate within the biofilm without

starving, ro and that after starving, rd. Based on Fig. 3

and Eq. (13), we found b ¼ ln (0.0074/0.0064)/

30 ¼ 0.00484 h�1. Then we found bdet ¼ 0–0.03 d�1

based on Eqs. (15) and (16); and kd ¼ 0.09–0.12 d�1

based on Eq. (14).

The yield coefficient, Y can be calculated based on

Eqs. (14) and (17) and using the parameters obtained

under BSSC1. At this condition, the actual measured

nitrate-N concentrations in the influent and effluent

were S0 ¼ 32.92, and Se ¼ 5.23mg/l. Therefore, the

nitrate-N concentrations of Sin and Savg were 5.912

and 5.564mg/l, respectively. The corresponding nitrate-N

ARTICLE IN PRESSH. Zeng, T.C. Zhang / Water Research 39 (2005) 4941–4952 4949

flux Jexp was 0.0005692mg–N/cm2-h. In this case, bdetwas calculated as 0.0154 d�1, and b was equal to 0.10–

0.13 d�1. Therefore, we estimated Y ¼ 0.19–0.25mg

VSS/mg NO3� ( ¼ 13.87� 0.0084� 0.00417/[0.0005692

� (62/14)] –13.87 � 0.0084� 0.00542/[0.0005692� (62/

14)]), or 0.85–1.11mg VSS/mg NO3�–N.

4. Discussion

From the literature, the recommended ranges of

kinetic parameters of autotrophs including nitrifying

bacteria are listed in Table 6: mm ¼ 0.005–0.11 h�1;

kd ¼ 0.05–0.15 d�1. The mm and kd obtained in this study

43.5

44

44.5

45

46

46.5

45.5

Time, min

0 50 100 150 200 250 300

y = -0.0064x + 46.13 R2 = 0.98

Before starving

After starving

y = -0.0074x + 45.66R2 = 0.96

S, m

g/L

Fig. 3. Time course of nitrate-N concentration, S, in the batch

reactor used for kd estimation before and after 30-h starving.

Table 6

Comparison of kinetic parameters

Sources

Parameters Claus and

Kutzner (1985)

Batchelor and

Lawrence (1978)

H

(

Bacteria Suspended Suspended S

Reactor CSTR CSTR C

S source S2O32� S0 powders S

Ks 0.045mg/l

NO3–N

0.03mg/l

NO3–N

N

k 0.176 g NO3–N/g

cells-h

NA N

mm 0.11 h�1 NA N

Y 0.57 g cells/g

NO3–N

b0.66 g cells/g

NO3–N

b

N

kd NA NA 0

NA ¼ not available.aFrom Henze et al., 1995.bConverted from 0.084mg organic-N/mg NO3–N in Batchelor and

al. (1985) assuming cell formula C5H7O2N.cFrom Botrous, 1999.

are within these ranges. In addition, our estimated kdand Y are consistent with other previous reported values

(Batchelor and Lawrence, 1978; Justin and Kelly, 1978;

Claus and Kutzner, 1985; Hashimoto et al., 1987).

Considering that errors on the calculation of b could be

caused by the 73% errors in HPLC measurements, the

possible range of kd could be from 0.00183 to

0.00584 h�1, or 0.04 to 0.14 d�1. Then the corresponding

range of Y would be 0.58–1.40mg VSS/mg NO3�–N or

0.13–0.32mg VSS/mg NO3. These ranges are still

consistent with the previous studies except that the

highest possible value of Y is relatively high (Table 6).

In the batch tests for kd and Y estimation, specific

denitrification rates were calculated ranging between

0.04 and 0.07mg NO3–N/mg VSS-d when fed with

artificial groundwater of 50mg/l NO3–N. These values

are a little lower than those reported before (Batchelor

and Lawrence, 1978; Hashimoto et al., 1987). The

difference can be explained by the very thin biofilm

cultured by 5mg/l NO3–N in this study. Combining

these four kinetic parameters evaluated in this study, the

minimum substrate concentration (Rittmann et al.,

1986), Smin (M/L3) ¼ Kskd/(mm–kd), for sustaining stea-

dy-state biomass is 2.4mg/l NO3–N, which was satisfied

in this study.

Our estimated Ks value is one order of magnitude

higher, and our k is two orders of magnitude lower than

the previous reported values (Table 6). This might be

attributed to several reasons. First, studies in Batchelor

and Lawrence (1978) and Claus and Kutzner (1985)

used a strain of pure culture of Thiobacillus denitrificans,

while we used a mixed culture in this study. Autotrophic

ashimoto et al.

1985)

This study Recommended range

for autotrophs

uspended Biofilm

STR CSTR and batch0 powders S0 particles

A 0.398mg/l

NO3–N

NA

A 0.0062 g NO3–N/

g VSS-h

NA

A 0.006 h�1 c0.005–0.104 h�1

0.62 g cells/g

O3–N

0.85–1.11 g VSS/

g NO3–N

NA

.058 d�1 0.09–0.12 d�1 a0.05–0.15 d�1

Lawrence (1978) and 0.33mg-TOC/mg NO3–N in Hashimoto et

ARTICLE IN PRESSH. Zeng, T.C. Zhang / Water Research 39 (2005) 4941–49524950

denitrifying bacteria might have co-existed, as a small

portion of the biofilm, with other bacteria (Koenig et al.,

2005); some heterotrophic denitrifiers might have been

able to grow in our reactors as was reported previously

(Lawrence, 1978; Zhang, 2002). Koenig and Liu (2004)

reported that the average specific denitrification rate

obtained from batch tests using S0 particles (2–2.8mm)

to treat wastewater of high-salinity was 0.006–0.008 g

NO3�–N/g VSS-h. In their tests, an influent of 100mg

NO3�–N/l was used, which was much higher than Ks

(Table 6). Therefore, the specific denitrification rate in

their tests was probably close to or the same as the

maximum specific denitrification rate, k. Our estimated

k value (0.006 g NO3�–N/g VSS-h) is consistent with

theirs, which may be because their system was a mixed

culture one. Therefore, our kinetic parameters do not

refer to pure cultures of autotrophic denitrifying

bacteria. This can be one of the reasons for us to have

a much higher Ks and a much lower k.

Second, Claus and Kutzner (1985) used S2O32� which

is more easily utilized by denitrifiers as compared with

S0 due to the limitation in the sulfur dissolution rate at

room temperature. In this study, we used S0 particles

with diameters between 2.38 and 4.76mm. The S0

powders used by Batchelor and Lawrence (1978, average

diameter ¼ 84 mm) and Hashimoto et al. (1987,

50–100mm) are much smaller, which may be one of the

reasons that their Ks values is close to Claus and

Kutzner’s but much lower than ours.

Third, their reactors (Batchelor and Lawrence, 1978;

Claus and Kutzner, 1985; Hashimoto et al., 1987) were a

suspended-growth system while ours were an attached-

growth one where the kinetic parameters within the

biofilm might have been altered from those of the

suspended-growth process (Harremoes, 1976; LaMotta,

1976; Hooijmans et al., 1990). Hydraulic conditions

(e.g., mixing pattern, molecular diffusion vs. convection,

etc.) would affect estimation of kinetic parameters

(Harremoes, 1976; Hooijmans et al., 1990). In addition,

different operation conditions (e.g., the sulfur powder

diameter, the reactor type, etc.) might result in different

biofilm thickness and biomass density, which would

affect the substrate utilization rate and estimation of

kinetic parameters. The physiology of cells may be

changed with the aggregate of cells, the exposure to

different concentrations of substrate, or the kinetic

parameters behave as the average of those exposed to

fresh substrate and those near to the attachment surface.

The above discussions indicate that our results may

reflect the actual environment that autotrophic denitri-

fiers will encounter in a fixed-bed SLAD process even

though the Ks and k values may not be the intrinsic

metabolic rate in the cells.

While previous studies did provide useful information

on the kinetics of autotrophic denitrification by Thio-

bacillus denitrificans, their results are mainly related to

processes with sulfur powders or thiosulfate as the sulfur

source. This study compensates previous studies because

in engineering practice it is highly possible that fixed-bed

SLAD biofilm processes will be used frequently. The

kinetic parameters obtained in this study provide

information that is useful for designing and evaluating

a SLAD biofilm system based on Monod-based kinetics

(e.g., reactor depth, relationship between nitrate re-

moval and the nitrate or hydraulic loading rate, etc.).

Results of this study can also be used for comparing the

SLAD biofilm process with other denitrification systems

based on Monod kinetics or predicting the performance

of a SLAD biofilm system, and compare these predic-

tions with special cases, such as zero-, one-half-, or first-

order autotrophic denitrification.

Considerable research has been conducted on biofilm

kinetics (Rittmann and McCarty, 2001). Determination

of kinetic parameters has historically been a tedious and

labor-intensive undertaking (Grady, 1985). To our

knowledge, most studies estimated biofilm kinetic

parameters based on curve fitting techniques, such as

fitting a mathematical model with axial substrate

concentration profiles along the column (Requa and

Schroeder, 1973; Kuba et al., 1990; Coelhoso et al.,

1992), or substrate concentration profiles within the

biofilm or immobilized enzyme (Hooijmans et al., 1990),

or substrate time courses within a batch reactor

contained biofilm stripped off from the media or still

attached on the media (Williamson and McCarty, 1976;

Lee and Dahab, 1988; Fox and Suidan, 1990). One

contribution of this study is that we combined the two in

situ techniques and used them to estimate the four

Monod-type kinetic parameters in a SLAD biofilm

system. Our method may also be suitable for estimation

of kinetic parameters in other biofilm processes.

However, cautions must be given when the para-

meters estimated from this study are used. First, biofilm

thickness (Lf) and biomass density (Xf) are very im-

portant for estimation of kinetic parameters. Table 7

lists how the kinetic parameters respond to the variances

of Lf if the method developed in the present study is

used. Biomass density (Xf) is the most sensitive parameter

to Lf, and k and Ks are the second and third most sensitive

parameter. kd and Y are not sensitive to Lf. Since the

estimated biofilm thickness fluctuated around the average

value as much as up to770%, it would be possible for the

k value to range from 0.00417–0.00917mg-N/mg-VSS-h,

which is very close to the range (0.00292–0.0104mg-N/mg-

cells-h) obtained from the SLAD process with a mixed

culture (Lawrence, 1978).

Second, in this study, biomass measurement was not

easy because (a) it was difficult to strip off the biomass

completely from sulfur and limestone particles since

sulfur stones were fragile; (b) it was observed that

biomass was not fully covering the particle surface,

which could cause the inaccuracy of the estimation of Lf;

ARTICLE IN PRESS

Table 7

Sensitivity analysis of Lf on biomass density and kinetic parameters estimation

Independent variable Dependent variables Change

Change (%) Lf (cm) Xf (mg/ml) Lf� Ks (mg/ml) K (1/d) Kd (1/d) Y Xf (%) Ks (%) k (%) kd (%) Y (%)

�70 0.0025 46.61 0.16 0.000447 0.099 0.12 0.22 �236.0 12.2 �33.4 0.0 0.0

�30 0.0059 19.75 0.25 0.000447 0.117 0.12 0.22 �42.4 12.2 �21.2 0.0 0.0

�10 0.0076 15.33 0.45 0.000447 0.144 0.12 0.22 �10.5 12.2 �3.1 0.0 0.0

0 0.0084 13.87 0.5 0.000398 0.149 0.12 0.22 0.0 0.0 0.0 0.0 0.0

10 0.0092 12.67 0.5 0.000447 0.183 0.12 0.22 12.2 12.2 22.9 0.0 0.0

30 0.0109 10.69 0.55 0.000398 0.193 0.12 0.22 8.7 0.0 29.8 0.0 0.0

70 0.0143 8.15 0.6 0.000398 0.220 0.12 0.22 41.2 0.0 48.3 0.0 0.0

�Lf was first assumed by different percentages, and then other dependent variables were calculated in the exact same way as the

experimental results were obtained in this study.

H. Zeng, T.C. Zhang / Water Research 39 (2005) 4941–4952 4951

and (c) during the relatively long period of biofilm

growth (�40 days), a portion of the biofilm in our

reactor should have consisted of non-active cells, which

was difficult to be differentiated from the active portion

of the cells. Therefore, the measured Xf could over-

estimate the actual active biomass. Both Lf and Xf could

possibly affect the results to a great extent. The accuracy

of the estimated kinetic parameters could be improved

should these problems be solved.

Finally, the results of this study are based on an

assumption that sulfur is not a limiting substrate in the

whole range of the test conditions regarding biofilm

thickness, density, and nitrate-N loading rates. When

the biofilm of a SLAD fixed-bed is very thick, it is not

known if sulfur will be a limiting substrate or not. The

important issue is that, at what range of biofilm

thicknesses will the biofilm thickness become saturated

with sulfur so that sulfur no longer affects nitrate flux? A

rough estimation can be made as follows. According to

Batchelor and Lawrence (1978), there was no indication

of sulfur saturation of the biofilm for experiments

conducted with a sulfur to biomass ratio, S/X, as high as

194mg S/mg organic-N. Based on S=X ¼ 194, a critical

biofilm thickness Lf(c) ¼ 84 mm if we assume (a) the

average diameter of spherical S grains ¼ 84 mm, (b)

sulfur density ¼ 2 g/cm3, (c) organic-N/VS ¼ 0.124 g/g

(i.e., the biomass composition ¼ C5H7O2N), and (d)

biofilm density (Xf) ¼ 13.87mg VS/cm3 (Batchelor and

Lawrence, 1978; Table 1]. Therefore, if a biofilm

thickness is oLf(c), it would be saturated with sulfur.

Because the calculated Lf(c) is very close to the Lf of the

reactor at the BSSC1 in this study, sulfur could be a

limiting substrate within the biofilms used for Ks and k

estimation.

It should be pointed out that in a slurry reactor, sulfur

powders tend to be floating on top of the solution even

when the solution is mixed very intensively. As the

amount of S/X increases a larger fraction of sulfur will

not be incorporated into a biofilm matrix (Batchelor and

Lawrence, 1978), while this is unlikely to happen in a

fixed-bed S/L column. Therefore, the reported S/X ratio

for a slurry reactor could be much higher than that for a

fixed-bed reactor, meaning that in a fixed-bed reactor

the Lf(c) could be much thicker than 84 mm. In S/L

columns, a higher nitrate-N loading would always result

in a thicker biofilm; the biofilm thickness decreases with

a decrease in nitrate concentration along the reactor

(Liu, 1992; Flere and Zhang, 1999), indicating that

nitrate, not S0 being the limiting substrate. Koenig and

Liu (1996) reported that the maximum area loading rate

was the process limiting factor for nitrate removal in a

S0 fixed-bed column, and is practically independent of

sulfur particle size. These results prove indirectly the

assumption of sulfur being a non-limiting substrate.

However, there is no direct experimental evidence to

further prove the assumption. Therefore, the results of

this study may be only applicable to elemental sulfur

denitrification systems that are operated to have a

similar biofilm thickness, as the one used in this study,

for estimation of the kinetic parameters.

5. Conclusions

In this study, four kinetic parameters of autotrophic

denitrifiers in fixed-bed SLAD column reactors were

evaluated. The kinetic parameters and methods developed

in this study can be used to facilitate modeling, design, and

evaluation of a SLAD biofilm process or to compare the

SLAD system with other denitrification technologies. The

methodology of combining the two in-situ techniques for

kinetic studies may also be suitable for estimation of

kinetic parameters in other biofilm processes.

Acknowledgements

The authors would like to thank Mr. Kent W.

Smothers and Ms. Jennifer Tester of the Midwest

ARTICLE IN PRESSH. Zeng, T.C. Zhang / Water Research 39 (2005) 4941–49524952

Technology Assistance Center (MTAC), Illinois State

Water Survey, for their management and support of the

project. The Midwest Technology Assistance Center

(MTAC), Illinois State Water Survey funded this

project, which is greatly appreciated.

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