Water Qual. Res. J. Canada, 2003
Volume 38, No. 1, 183–192
Copyright © 2003, CAWQ
A Kinetic Model for Autotrophic Denitrification
using Sulphur:Limestone Reactors
ASHREF DARBI AND THIRUVENKATACHARI VIRARAGHAVAN*
Faculty of Engineering, University of Regina, Regina, Saskatchewan, Canada
The kinetics of autotrophic denitrification of groundwater by Thiobacillus
denitrificans in a sulfur:limestone upflow reactor was examined in order to predict effluent concentrations. Experiments were performed using water containing 60 and 90 mg NO3—N/L and sulfur and limestone with average particle size
of 3.5 mm. Results clearly showed that nitrate was completely removed from 60
and 90 mg NO3—N/L influent concentrations. The results showed that the
autotrophic denitrification rates in sulfur:limestone reactors can be described
by half-order kinetics. The half-order reaction rate constants for the entire
media were estimated at 1.34 and 1.54 mg1/2/L1/2 h for influent concentrations of
60 and 90 mg NO3—N/L, respectively.
Key words: autotrophic denitrification, nitrate removal, Thiobacillus denitrificans, sulfur, limestone, drinking water, kinetics
Introduction
Numerous water agencies face problems of increasing concentrations
of nitrate in groundwater. The main reason for increasing nitrate concentrations in groundwater is the extensive application of artificial fertilizers
and animal manure in agriculture. The contamination of groundwater by
excessive concentrations of nitrate is a significant public health problem.
Infant methemoglobinemia is known to occur when nitrate-nitrogen in
drinking water exceeds 10 mg/L (Packham 1992). The Canadian drinking
water standard for nitrate is 10 mg/L as nitrate-nitrogen (Guidelines for
Canadian Drinking Water Quality 1996). A wide range of physico-chemical processes such as ion exchange, reverse osmosis and electrodialysis,
biological denitrification and chemical denitrification, are currently in use
or under development for the removal of nitrates from drinking water
(Kapoor and Viraraghavan 1997). Methanol is often added for nitrate
removal by heterotrophic denitrification since the availability of organic
carbon is limited in drinking water (Hoek et al. 1987). As an alternative,
autotrophic denitrification using Thiobacillus denitrificans can reduce
nitrate to nitrogen gas while oxidizing elemental sulfur to sulfate.
Limestone is used to maintain the pH and provide an inorganic carbon
* Corresponding author; [email protected]
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DARBI AND VIRARAGHAVAN
source for the bacteria. The reaction proceeds as follows (Batchelor and
Lawrence 1978; Schippers and Kruithof 1987):
55S + 50NO3- + 38H2O + 20CO2 + 4NH+4 →
4C5H7O2N + 25N2 + 55SO2-4 + 64H+
(1)
Further practical application of autotrophic denitrification requires a
kinetic model. Data on concentration profiles available from experiments
made by Sutton (1973) at 20°C showed that the data fitted the half-order
reaction and gave volume removal rates in the range of 0.08 to
0.14 mg1/2/L1/2 min and surface removal rates between 1.3 and 2.2 x
10-3 mg1/2/L1/2 min for 13-mm ceramic intalox saddles. The scatter of the
data at other temperatures made conclusions on the order of reaction difficult (Harremoës 1976).
Harremoës and Riemer (1975) examined a large number of profiles
with different hydraulic loadings on a pilot-scale downflow filter with a
3- to 4-mm gravel medium. When the removal rate per unit volume was
plotted against the nitrate concentration, they found that a half-order
reaction fitted the data well. Batchelor and Lawrence (1987) developed a
kinetic model to describe continuous flow reactors with elemental sulfur
biomass slurries. LeCloirec (1985) developed a mathematical model for
denitrification by Thiobacillus denitrificans in a sulfur:limestone (S:L) reactor. However, none of these models are easily applicable to predict nitrate
profiles and effluent nitrate concentrations in the upflow sulfur:limestone
reactor. Koenig and Liu (2001) conducted experiments using autotrophic
denitrification of synthetic wastewater by Thiobacillus denitrificans in
upflow sulfur packed-bed reactors. The experimental results showed that
autotrophic denitrification by the biofilm in the reactors can be described
by a half-order kinetic model.
A batch study made by Koenig and Liu (2002) showed that in the
case of autotrophic denitrification with sufficient alkalinity (initial alkalinity of 680 mg/L as CaCO3), nitrate concentration decreased linearly
with time and autotrophic denitrification followed first-order kinetics.
The objectives of this study were to examine the use of a suitable
kinetic model for upflow sulfur:limestone reactors, and to determine the
kinetic constants for reactors with different nitrate-nitrogen concentrations and compare the results with other studies.
Materials and Methods
Thiobacillus denitrificans Culture
Thiobacillus denitrificans (ATCC 23642) was grown in a medium as
described by Lampe and Zhang (1996). The composition of the medium
was 6 g/L Na2S2O3.5H2O, 3 g/L KNO3, 1.5 g/L NaHCO3, 1.5 g/L
Na2HPO4, 0.3 g/L KH2PO4, 0.4 g/L MgSO4.7H2O and 1 mL/L trace nutrient solution. The composition of the trace nutrient solution was
SULPHUR: LIMESTONE REACTORS
185
56.25 mg/L K2HPO4, 5.74 mg/L NH4Cl, 1 mg/L MgCl2.6H2O, 1 mg/L
MnSO4.H2O, 1 mg/L CaCl2 and 1 mg/L FeCl2.6H2O. The stock culture
was inoculated into 1 L of medium, flushed with nitrogen and incubated
at room temperature for 7 to 14 d.
Column Studies
A (2:1) sulfur:limestone (mass/mass) reactor (Fig. 1) was used in the
column study. This same reactor had a nitrate removal rate of approximately 100% at the end of one year of operation. The column was under
continuous operation with a flow rate of 2 mL/min. The results showed
that the nitrate removal efficiencies were almost exactly the same over a
period of six months, indicating that the reactor had reached steady-state
conditions.
Earlier detailed column studies have shown that 2:1 (mass/mass) is
the optimum S:L ratio; under a hydraulic retention time (HRT) of 13 h,
nitrate concentration of 60 mg NO3—N/L was reduced to less than 5 mg
NO3—N/L (Darbi et al., Unpublished).
Tap water was used to prepare two different initial nitrate concentrations (60 and 90 mg NO3—N/L); the sulfur and limestone particles
both had a mean particle size of 3.5 mm. Characteristics of the tap water
are shown in Table 1. The reactor was fed continuously in the upflow
mode by peristaltic pumps. All experiments were conducted at room temperature of 21 ± 1°C. Samples were collected for analysis from the influent, the three sampling ports and the effluent.
Fig. 1. Upflow fixed-bed column reactor.
186
DARBI AND VIRARAGHAVAN
Table 1. Tap water characteristics
Parameters
Tap water
pH
Conductivity, µS/cm
NO3—N, mg/L
NO2—N, mg/L
Cl-, mg/L
SO4—, mg/L
Hardness, mg/L as CaCO3
Alkalinity, mg/L as CaCO3
TDS, mg/L
7.5
534
0
0
18
185–200
232
124
230
Specific surface areas of sulfur and particles were determined using
a Flowsorb II 2300 manufactured by Micromeritics Instrument
Corporation, Georgia, U.S.A. Single point surface area measurements
were carried out using a gas mixture of 29.0 M % nitrogen and 71.0 M %
helium. Liquid nitrogen was used to set the temperature for adsorption of
nitrogen gas by the samples. Specific gravity and porosity of the media
were determined to be 2.03 and 0.42, respectively, using methods
described in American Society for Testing and Materials (ASTM 1991).
Kinetics
As the Monod saturation constant (Ks) for autotrophic denitrification
was reported to be low (Claus and Kutzner 1985; Batchelor and Lawrence
1987), the intrinsic reaction inside the biofilm can be taken as zero-order.
Since the penetration of substrate in the pores of biofilm is less than fully
effective, a zero-order reaction in the biofilm becomes a half-order reaction at the surface of biofilm (Koenig and Liu 2001).
Assuming the filter as a plug flow reactor:
∂C
A
= – rv
∂Y
Q
(2)
where C is concentration, Y is distance from the entrance, Q is flow rate,
A is cross-sectional area, and rv is removal rate per unit volume of the filter.
A partially efficient biofilm will result in a half-order reaction:
rv = k1/2 v C1/2
(3)
SULPHUR: LIMESTONE REACTORS
187
where k1/2 v is the half-order reaction constant per unit volume of the
reactor.
–
∂C
= – kC1/2
∂t
(4)
(5)
1/2
1/2
Ce =C 0
-
1
k
t
2 1/2v H
(6)
where Ce is effluent concentration, C0 is influent concentration, and
tH is the empty bed residence time = AH/Q (H = height of reactor).
The profile should be a straight line in a plot of C1/2 versus tH. The
half-order reaction rate per unit volume can be calculated from the slope
of the line. The specific surface area of the filter media is ω which was estimated by multiplying the specific surface area of the particles by the factor (1-ε) where ε is the porosity of the reactor.
k1/2 v = ω k1/2 a
(7)
Where k1/2 a is the half-order surface reaction rate of the biofilm and
ω the specific surface area of the reactor media.
Results and Discussion
Column Studies
The column contained sulfur and limestone media with a ratio of 2/1
mass/mass and all kinetic constants calculated were for all the media. The
limestone provided buffering capacity and was the major inorganic carbon source for the S:L system (Flere and Zhang 1999). Figure 2 shows
clearly that nitrate was completely removed under both initial concentrations of 60 and 90 mg NO3—N/L. The figure shows the reduction of
nitrate concentration as a function of residence time. A plot of square root
of nitrate concentration versus empty bed residence times shows a
—
straight line. Plotting √C in mg1/2/L and T in h gives the following
dimensions for the volume rate k1/2v = mg1/2/L1/2 h. Figure 3 provides a
plot between the square root of nitrate concentration and HRT using the
data from Fig. 2. The relationship was found to be linear, with a correlation coefficient of nearly 1.0. Using equation 7 the half-order reaction rate
constants for reactor media can be estimated. Table 2 shows the k1/2a to be
0.018 and 0.020 mg1/2/dm1/2 h for influent concentrations of 60 and 90 mg
NO3—N/L, respectively.
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DARBI AND VIRARAGHAVAN
Fig. 2. Nitrate concentration profile through the
column for 60 and 90 mg NO3––N/L.
Fig. 3. Square root of nitrate concentration versus
HRT for 60 and 90 mg NO3––N/L.
S
Koenig and Liu (1997)
2.8–5.6
2.8–5.6
5.6–11.2
11.2–16
2.38–4.76
2.38–4.76
Medium
size, mm
0.40
0.40
0.40
0.40
0.421
0.421
Porosity
2.36–3.52
2.94–3.6
1.49–2.04
1.12–1.34
1.34–1.54
1.89–2.17
k1/2v
mg1/2/L1:2 h
81.82
81.82
42.86
26.47
76.6
76.6
ω
dm2/dm3
0.029–0.043
0.036–0.044
0.035–0.047
0.043–0.050
0.018–0.020
0.025–0.028
k1/2a
mg1/2/dm1/2 h
20–25
20–25
20–25
20–25
21±1
21±1
T°C
aA S:L ratio of 2:1 by mass would correspond to a S:L ratio by volume of about 2.5:1, i.e., 71% of the media volume consists of sulfur.
A k1/2v value of 1.45 for the mixed column would therefore correspond to a k1/2v value of 2.17 on the basis of a 100% sulfur column.
S
S
S
S+L
S
Type of
medium
Koenig and Liu (2001)
This study
This study
Refer.
Table 2. Comparison of half-order reaction rate constants for autotrophic denitrificationa
SULPHUR: LIMESTONE REACTORS
189
190
DARBI AND VIRARAGHAVAN
The plots shown in Fig. 3 clearly demonstrate the applicability of the
half-order reaction rate model. Table 2 also shows the data from other
sources in the literature. The results from this study are comparable to literature values where these rates are defined in terms of surface.
In this study, the reactor contained sulfur and limestone with a ratio
of 2:1 (mass/mass); in other studies, the medium was only sulfur. The
concentrations used in this study were 60 and 90 mg NO3—N/L, while in
the Koenig and Liu (2001) studies, the concentrations were different and
the porosity in this study was slightly different. Consequently, different
half-order reaction rate constants were obtained. The theoretical requirement of alkalinity for complete denitrification based on equation 1 is
427 mg/L as CaCO3. The autotrophic denitrification with sufficient alkalinity (680 mg/L as CaCO3) followed first-order kinetics (Liu and Koenig
2002). When the initial alkalinity decreased to 217 and 113 mg/L as
CaCO3 the slopes of nitrate profiles became lower indicating a gradual
decrease in the denitrification rates (Liu and Koenig 2002).
In these experiments, the result showed that the alkalinity in the raw
water was 145 mg/L as CaCO3 and increased to 196 mg/L as CaCO3 after
it passed through the bioreactor. These levels of alkalinity were insufficient to allow complete denitrification in the system.
Based on calculations using data from other sources in the literature
with filter sizes ranging from laboratory to full scale, media size from 3 to
28 mm, porosity from 0.4 to 0.9, with different shapes and with temperature from 6 to 27°C, surface rates varied from 1 to 10 x 10-3 mg1/2/dm1/2
min. This indicates that all filters functioned on the same principle: zeroorder reaction in pores that are only partly effective, resulting in overall
half-order reaction kinetics (Harremoës 1976).
Based on the analysis of the data with zero-, half- and first-order
reaction kinetics, it was also found that the half-order reaction rate fitted
the data well and the correlation coefficient was higher in this case than
with the other reaction orders (Table 3).
Conclusions
The half-order reaction model can be applied to describe a
sulfur:limestone autotrophic denitrification system. Nitrate concentra-
Table 3. Correlation coefficient of the reaction rates
Column 60 mg NO3––N
Column 90 mg NO3––N
Zero order
Half order
First order
0.81
0.87
0.93
0.96
0.92
0.75
SULPHUR: LIMESTONE REACTORS
191
tions of autotrophic denitrification using sulfur:limestone reactor can be
estimated using a half-order reaction equation:
Ce1/2 = C01/2 – 1– k 1/2 v t H
2
where k1/2v for the entire media in the column study is 1.34 and 1.54
mg1/2/L1/2 h for 60 and 90 mg NO3—N/L, respectively. The half-order
reaction rate constant depends on the specific surface area of the reactor
media. k1/2a is 0.018 and 0.20 mg1/2/dm1/2 h for influent concentrations of
60 and 90 mg NO3—N/L, respectively, for the column reactor.
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