Nitrification kinetics of activated sludge-biofilm system: A mathematical model

Bioresource Technology 101 (2010) 5827–5835

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Nitrification kinetics of activated sludge-biofilm system: A mathematical model Arun Kumar Thalla *, Renu Bhargava, Pramod Kumar Department of Civil Engineering, IIT-Roorkee, Roorkee 247 667, India

a r t i c l e

i n f o

Article history: Received 19 December 2009 Received in revised form 2 March 2010 Accepted 3 March 2010 Available online 24 March 2010 Keywords: AS–biofilm reactors Nitrification Mathematical model Substrate flux

a b s t r a c t Although activated sludge (AS)-biofilm system has many advantages, it lacks in the mathematical concepts for its design. This paper deals with deducing a mathematical model for the simulation of ammonical nitrogen in such systems starting from the basic mass balance equations. Monod kinetic equation and Fickian diffusion principles are coupled to derive the model. The model thus developed is solved numerically and validated with the experimental results obtained on a laboratory scale AS–biofilm system. It is found that the model validated well with the experimental results which was supported by the R2 value of 0.79, further the statistical analysis between the observed and predicted values for various experimental conditions showed that the model tends to under-predict at high removal efficiency, whilst a slight tendency towards over-prediction at low removal efficiency values. Fractional error plot for the NH4+– N data sets showed that the difference between observed and predicted values are insignificant at 5% level of probability for NH4+–N. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Presence of nutrients, especially nitrogen and phosphorus in wastewater may lead to eutrophication and depletion of oxygen content, and thus pose health hazards to aquatic life. The process of nitrogen removal from wastewater is a six-stage microbial reaction process: hydrolysis of organic nitrogen, ammonia oxidation, nitrite oxidation, nitrate reduction, nitrite reduction and nitrous oxide reduction. The nitrifying bacteria have slow growth rates and are sensitive to changes in environmental conditions such as temperature, pH and the composition and characteristics of wastewater (Metcalf and Eddy, 2005). AS–biofilm reactors proved to be the prudent technology for nitrification of wastewaters (Wanner et al., 1988; Baozhen et al., 1996; Randall and Sen, 1996; Muller, 1998; Gupta and Gupta, 1999; Andreottola et al., 2000; Münch et al., 2000; Watanabe et al., 1994). However, in order to improve the performance of the system keeping the foot print at its minimum, it is advisable to design the system as a number of reactors operated in-series. This paper deals with the development of mathematical model to describe the nitrification process in a AS–biofilm system. The models are developed, taking into consideration the basic equations of the hybrid reactor according to Monod kinetics expressions of both cultures simultaneously. More than one form

* Corresponding author. E-mail addresses: [email protected] (A.K. Thalla), [email protected] (R. Bhargava), [email protected] (P. Kumar). 0960-8524/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.biortech.2010.03.014

can be developed after rearranging these expressions based on the purpose for which the models are required. The models developed can be easily used as the modified expression for substrate flux into biofilm proposed by Fouad and Bhargava (2005), thus reducing the steps for evaluation of this variable. Knowledge of hydraulic retention time, influent substrate concentration, stagnant liquid layer thickness, minimum substrate concentration that can maintain the biofilm growth and kinetic constants permit computation of effluent substrate concentration and suspended biomass concentration. After computation of biomass concentration, other parameters such as food to biomass ratio and wasted mass of sludge can be obtained. Further the ratio of the active biofilm to the suspended biomass and the fraction of substrate used by any culture can be obtained. 2. Development of mathematical model The process diagram of an aerobic hybrid system is shown in Fig. 1(a) while Fig. 1(b) defines the process schematic used for the model development. The system is assumed to run under steady state condition for biomass production and substrate removal with a rate limiting substrate concentration through the reactor. The same kinetics has been assumed applicable to both suspended and attached growth systems (Lawrence and McCarty, 1970; Williamson and McCarty, 1976a,b; Rittmann and McCarty, 1980b; Livingston, 1991). In addition to the basic assumptions applicable for suspended and attached growths, the following assumptions have been considered in developing the model.

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Suspended biomass

QS , N S XS

Media for biofilm growth

Q0 , N0 X0

Q0 , N, X

Qe , Xe N

Qr, Xr, N

Qw, Xr

(a) Biomedia Q X N

S S S

(ii) (i)

Qo

Qo

Q0-Qw

Xo

X

Xe

No

N

N

Hybrid reactor

Settling tank

Q

r

X

r Qw X u

(b) Fig. 1. Components of AS–biofilm system. (a) Process diagram of AS–biofilm system and (b) schematic of the aerobic hybrid system.

2.1. Assumptions (1) All the microorganisms in the reactor are active for treatment and Monod type kinetic expression is valid to describe the biomass growth. (2) Biofilm has homogeneous structures and density (Gikas and Livingston, 2006, 2007). (3) Cell growth in the attached phase is expressed by Monod type expression (Gikas and Livingston, 1999). (4) Only one – space dimension perpendicular to the biofilm structure is considered. (5) Transport of the dissolved components in the liquid phase is by molecular diffusion and can be described by Fick’s law of diffusion (Duddu et al., 2009). (6) Stochastic phenomena can be neglected, i.e. that any random differences among the cells of a given type can be ignored. Considering the control volume (i) as shown in Fig 1(b), the mass balance equations for substrate (ammonical nitrogen) and biomass on the aerobic hybrid reactor may be written as

    dN VXkN V ¼ Q S ð1 þ RÞN 0  Q S ð1 þ RÞN  aVJ þ dt KN þ N   dX bs V ¼ Q S ð1 þ RÞX 0  Q S ð1 þ RÞX þ YaVJ dt bt   YkN þ VX  Kd KN þ N

ð1Þ

where dN/dt, the changing rate of ammonical nitrogen concentration in the bulk; QS, flow rate of the raw substrate (L3 T1); a, specific surface area of the biofilm (1/L); V, reactor volume (L3); k, maximum specific rate of ammonical nitrogen utilization (1/T); and KN, Monod half-velocity (M/L3); dX/dt, changing rate of biomass concentration in the reactor; Y, yield coefficient; bs, specific shear loss rates (1/T); bt, sum of specific decay and shear loss rates (1/ T); Kd, specific decay rate corresponding to nitrifiers (1/T); J, ammonical nitrogen flux (M/L2 T); R, recycle ratio; N0 and N, initial and final NH4+–N concentrations respectively from the reactor (M/ L3); X0 and X, initial and reactor biomass concentrations respectively (M/L3). Applying mass balance on the complete system for biomass, the expression will be

    dX bs YkN V ¼ YaVJ þ VX þ N  K d  ðQ w X u þ Q e X e Þ dt KN bt

ð3Þ

where (QwXu + QeXe) wasted mass of sludge (M/T). The boundary conditions for these mass balance equations are At the inlet to the reactor S

þRN N0 ¼ N1þR

)

S

þRX r X 0 ¼ X 1þR

ð4Þ

At the outlet or within the reactor

ð2Þ

N¼N X¼X

 ð5Þ

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where NS, raw substrate concentration (M/L3); XS, biomass concentration in the raw substrate (M/L3). At steady state, dN ¼ dX ¼ 0. dt dt Substituting this condition in Eq. (1), the resulting equation is:

 Q S ð1 þ RÞðN0  NÞ  V aJ þ



XkN ¼0 ðK N þ NÞ

ð6Þ

At steady state, after rearranging the variables in Eq. (2), the following expression for the biomass concentration is obtained:

ðbt Q S ð1 þ RÞX 0 þ YaVJbs Þ   bt ½Q S ð1 þ RÞ  KVYkN þ VK d  þN N

X¼

ð7Þ

Eq. (6) can be written as the sum of two equations to represent individually the suspended growth and attached growth systems. Substrate balance for suspended growth phase.

Q S ð1 þ RÞrðN 0  NÞ  V



 XkN ¼0 ðK N þ NÞ

ð8Þ

hC ¼ ¼

aVJ bYt þ XV S

YQ ð1 þ RÞðN0  NÞ  XVK d  aVJY Kbdt hh ðaJðY=bt Þ þ XÞ YðN 0  NÞ  Xhh K d  ahh JY Kbdt

ð16bÞ

The above models are developed, considering the basic equations of the hybrid reactor according to Monod kinetics expressions for both cultures simultaneously. The models in the present case were deduced for the evaluation of N, X, hC, food to microorganism ratio (F/M), (QwXu + QeXe) and R. Input parameters to the model are substrate residence time (h), influent ammonical nitrogen concentration (N0), thickness of the stagnant layer (L), and kinetic constants. Minimum substrate concentration (Nmin) that should be maintained in the reactor to maintain the biofilm growth is computed from the kinetic constants [Nmin = KNbt/(Yk  bt)]. N and X are computed by Eqs. (10), (13), and (14) by an iterative scheme. After computation of X, (QwXu + QeXe) can be obtained from Eq. (15). Further the fraction of substrate used by any culture can be obtained by Eq. (8), (9). By definition, food to biomass ratio (F/M) can be represented as

Substrate balance for attached growth phase.

Q S ð1 þ RÞð1  rÞðN0  NÞ  aVJ ¼ 0

ð9Þ

where ‘r’ represents the fraction of substrate that is used by suspended biomass in the reactor. By definition, the hydraulic retention time (hh) is the time for which the liquid stays in the reactor, whereas fresh substrate residence time (h) is the ratio between the volumes of the reactor to that of the flow rate. In mathematical terms,

h ð1 þ RÞ

hh ¼

h¼

ð10Þ

V

ð11Þ

QS

Hydraulic retention time is equal to fresh residence time under no recycle condition. Whence, using Eq. (6),

 ðN0  NÞ  hh aJ þ

X¼

 XkN ¼0 ðK N þ NÞ

ðb X þ Yahh Jbs Þ h t 0  i þ hh K d bt 1  hKhNYkN þN

ð12Þ

ð13Þ

Combining Eqs. (12) and (13), we get,

f ðNÞ ¼ ðN0  NÞ  ðaJhh Þ   ðhh kNÞ½Xbt þ YaJhh ðbt  K d Þ  bt ½Yhh kN þ K d hh ðK N þ NÞ þ ðK N þ NÞ

ð14Þ

F Q S ð1 þ RÞðN0  NÞ ¼ M ðaVJY=bt Þ þ VX

ð17Þ

The above Eq. (17) is used to compute the F/M. Moreover, the model enables the mean sludge residence time for the hybrid reactor (hC) to be evaluated by Eq. (16b). 3. Expression for substrate flux In order to simulate the above model, we need to know the flux parameter in addition to other parameters. According to Rittmann and McCarty (1980a), substrate transport from bulk water into a fixed biofilm is a diffusion controlled process, and there is a minimum substrate concentration (Nmin) that must be maintained in the bulk water to create a concentration gradient across the biofilm. Hence, the biofilm is inactive and is neglected when the substrate concentration approaches Nmin. Many models are available that relates the substrate flux (J) with effluent substrate concentration (N). To simplify the use of these mechanistic biofilm models, pseudoanalytical solutions have been developed that consists of a set of algebraic equations approximating the results of the numerical solution (Suidan and Wang, 1985; Sáez and Rittmann, 1988). The algebraic relationship between the flux of substrate and the concentration of substrate in the bulk liquid, as derived by Suidan and Wang (1985), is given by

   1:19 0:61 J 0:5J 2 þ J  1:0 þ 3:4    N ¼ J  L þ tanh NJ

ð18Þ

min

Using Eq. (3), the amount of sludge to be wasted at steady state, out of the system is given by the expression.

ðQ w X u þ Q e X e Þ ¼ YaVJ

  bs YkN þ VX  Kd KN þ N bt

ð15Þ

By the definition for sludge residence time (hC), it is the ratio between the total active biomass (suspended + attached) to that of total net production (Rittmann and McCarty, 2001).

total active biomass total net production suspended biomass þ mass of biofilm ¼ total net production

hC ¼

ð16aÞ

where N*, dimensionless effluent NH4+–Npconcentration = N/KN; J*, ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dimensionless ammonical nitrogen flux p ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J= K N kX f Df ; L*, dimensionless thickness of the stagnant layer = L ðkX f Þ=ðK N Df ÞðDf DW Þ; Nmin , dimensionless minimum substrate concentration = 1/(Yk(bt  1)). In which Df and Dw represent molecular diffusion coefficient (L2 T1) in biofilm and in water respectively. This model is one of the most widely accepted models for describing the biofilm flux. Many reactors under different cases can be described using this model. Suidan et al. (1989) has proposed a graphical solution for the above equation which is obtained for a chosen values of L* and N min . In order to eliminate the interpolations and human errors involved in reading the curves, Fouad and Bhargava (2005) have proposed a simplified expression to compute the biofilm flux which is

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ðJ  Þ0:88 ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðL Þ1:76 þ 5:2ðN   Nmin Þ  ðL Þ0:88 2:6

for N min

< 10

ð19Þ

J  ¼ ðN   Nmin Þ=ð4:5N  þ L Þ for Nmin > 10

ð20Þ

where Nmin = KNbt/(Yk  bt).

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J  ¼ J= K N kX f Df

ð21Þ

For computing J, modified substrate flux expressions proposed by Fouad and Bhargava (2005) as presented by Eq. (19)–(21) have been adopted in the present study. 4. Solution for the model As discussed above, the developed models can be used to determine the operating parameters viz. N, X, hC, F/M, (QwXu + QeXe) and R. However, to solve the model, we need to first compute the effluent substrate concentration which is a function of flux and biomass concentration. In order to determine the effluent substrate concentration from the system, initial boundary values have been determined by solving expression Eq. (14) numerically (regular falsi method). Once the effluent concentration is determined, the above said parameters can be determined by using Eq. (13)–(15), (16a), (16b), (17). Fig. 2. (a) Lab scale activated sludge – biofilm reactor. (b) Media (BioflowÒ 9) used for attached growth in AS–biofilm system.

5. Laboratory experiments Studies on AS–biofilm reactor were conducted at INRA-LBE, Narbonne, France.

Table 1 Characteristics of vinesse waste.

5.1. Experimental model

Parameter

Value

pH Sulfate CODT CODS Total suspended solids Total volatile solids NH4+ (mg N/L)

4.3–4.5 45–50 19,000–30,000 18,000–28,500 1850–3700 1009–1914 16–17

an important parameter in the design of biofilm-activated sludge reactors which is a function of L*, N* and N min .

A 5 L double walled bio-reactor was used in the present study. The reactor was equipped with air diffusers (spiral) to spurge DO into it; an air pump that could be regulated by a valve to adjust the air flow served the purpose. pH and DO probes were fitted to the reactor to monitor their variations in the reactor. The contents of the reactor were mixed well by means of the magnetic stirrer. Three peristaltic pumps were used for maintaining the inflow, out flow and recycling of the contents. The system was operated for two conditions by varying the type and quantity of media. A 5 L settler was used as settling unit. The experimental setup is shown in Fig. 2(a).

Table 2 Overview of the phase three experiments. Parameters

Descriptions

Reactor configuration Wastewater feed to reactor Movable media % of media filling Temperature Rate of recirculation Operating conditions

One reactor operated in continuous mode

BioflowÒ 9 30% of Reactor volume 35 + 2 °C Recirculation ratio was adjusted based on the MLVSS concentration in the reactor Continuous feeding of the reactor started with initial OLR of around 0.5 kg COD/m3 d and then OLR was increased gradually by increasing the substrate concentration and also by decreasing HRT

Seeding

Municipal wastewater treatment unit at Narbonne (100% reactor volume)

Vinasse based synthetic wastewater

Analysis performed

Daily analysis Total COD (CODT) pH Temperature NH4+–N NO2–N NO3–N Twice a week analysis Volatile suspended solids (VSS) Analysis at the end of experiments Biomass quantification Total solids (TS) Volatile solids (VS)

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of feed composition is changed by changing the ratio between the vinesse and tap water.

5.2. Biofilm carriers Bioflow 9 manufactured by RauschertÒ, a German company shown in Fig. 2(b) was used as media in the study. The characteristic properties of the medium were 9 mm high, 7 mm diameter with density and specific surface area 45 kg/m3 and 800 m2/m3 respectively. The quantity of Bioflow 9 media incorporated into the rector was about 30% of the reactor volume.

5.3. Synthetic sample Vinesse (the effluent of winery distillery) was used to prepare synthetic wastewater. The chemical and physicochemical characteristics of the vinasse are shown in Table 1. The substrate is prepared by diluting the vinesse with tap water and adding urea, KH2PO4 (source of nitrogen and phosphorous) and MgSO4 resulting in a mass ratio of COD/N/P = 300/10/1. Concentration of MgSO4 in the feed was 50 mg/L throughout the studies. The concentration

5.4. Operation The reactor was seeded with activated sludge collected from the Municipal Wastewater Treatment unit at Narbonne (France) having a volatile suspended solids concentration of 3 g/L. Bioflow 9 media in the proportion of 30% of the reactor volume was incorporated into the reactor. The reactor was operated with 100% recycling till a steady state was reached. The reactor was fed with variable organic loading rates by varying the influent concentrations. The reactor was operated in continuous mode with recycle and COD/N/P ratio of 100/10/1. The MLVSS in the system was maintained around 1.5–3 g/L throughout the study so as to give a way for the attached bacteria to carry out the decomposition. The experimental conditions during the course of the experiment have been summarized in Table 2. Dissolved oxygen concentration

2 1.75

Xθ / (N0 -N), day-1

1.5 1.25

1

Ks /k =0.2511 mg/L-d Ks = 0.27 mg/L

(1/ K) =0.93

0.75 0.5 0.25 0

0

0.5

1

1.5 2 1 / N, (mg/L)-1

2.5

3

3.5

(a) 0.4

1/θ, day-1

0.3

0.2 Y = 0.39 0.1

0

-Kd = -0.04 Kd=0.04 d-

-0.1 0

0.2

0.4

0.6

0.8

1

(N0-N) / (X θ), day-1

(b) Fig. 3. Plot for the determination of (a) KN and k (NH4+–N) and (b) Y and Kd (NH4+–N).

1.2

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Fig. 4. Determination of NH4+–Nmin – reactor operated under pure attached growth phase.

in this complete study was maintained in between 4 and 6 mg/L. Complete analysis of anion, cation, COD and volatile suspended solids were analyzed.

6. Parameter estimation To evaluate the kinetic parameters in addition to reactor performance with respect to nitrogen removal at 30% filling, the reactor was operated with vinesse based synthetic wastewater in three phases (i) pure suspended growth (for obtaining k, KN, Y and Kd) (ii) pure attached growth (for obtained Nmin and Xf) and (iii) combined growth phase.

6.1. Results on combined process At the beginning of the experiment, the reactor was operated at 15 h HRT. The HRT was then stepwise reduced to 6 h. At an average HRT of 15 h, the influent COD concentration was gradually increased from 297 to 750 mg/L. It was observed that the COD removal efficiency was as high as 94% when the feed COD was 297 mg/L. With increase in COD concentration, keeping all other parameters constant, the COD removal efficiency came down to 87%. Average ammonical nitrogen removal efficiency was around 95% during these studies. The COD concentration was then kept constant around 1000 mg/L and the HRT was then reduced to 10 h after 46 days when the system attained a stable condition. The studies were carried out with this HRT for about 27 days (78th day). The average percentage removal efficiency of total and soluble COD was 90% while percent removal of ammonical nitrogen was observed to be close to 98%. Further reduction in HRT to 6 h did not show any considerable change in the performance of the system i.e. the COD and NH4+–N removal efficiencies were maintained at 90% and 96% respectively. This high percent removal of ammonical nitrogen could be due to the maximal activity of nitrifying biofilm on the material support. The data collected on the system was used to evaluate the parameters. From the structure of the model, it is seen that parameters k, KN, Y, Kd, bs, Dw, Df, Nmin and L are to be known a priori in order to verify the model. Parameters Dw, Df, and L were taken from the literature.

6.2. Suspended growth kinetic parameters The reactor was run under pure suspended growth phase for 12 runs at DO of 2.5–3.5 mg/L and N0, N, X, NH4+–N, NO 3  N and NO 2  N were observed. As shown in Fig. 3(a), the values of Xh=ðN 0  NÞ and 1/N when plotted for each run give a straight line with slope 0.251 and intercept 0.93 representing KN/k and 1/k respectively. Whence, KN and k are computed as 0.27 mg NH4+–N/L and 1.076 d1 respectively. Similarly, from Fig. 3(b), the plot 1/hC vs. ðN 0  NÞ=Xh is a straight line with slope 0.39 and intercept 0.04 which represent Y and Kd respectively, from which the values of Y and Kd works out to be 0.39 and 0.04 d1 respectively. 6.3. Attached growth parameters Substrate transport from bulk liquid to biofilm depends on diffusion characteristics and there is a critical limit of substrate concentration below which the biofilm is ineffective. In other words, there is a minimum substrate concentration that must be maintained in the bulk water to create a concentration gradient across the biofilm and to support adequate amount of heterotrophs and autotrophs (Rittmann and Mccarty, 1980a; Gikas and Livingston, 1997). In order to determine this parameter, the reactor was run under pure attached growth phase by regulating the flow in such a way that

Table 3 Kinetic parameters for the vinesse synthetic wastewater.

*

Parameter

NH4+–N balance

Estimation

KN (mg/L) k (d1) Y Kd (d1) bt bs (d1) Nmin a (1/cm) Xf (mg/cm3) Df (cm2/d) Dw (cm2/d) L (cm)

0.27 1.076 0.39 0.04 0.19 0.15 0.223 2.24 0.49 1.04 1.3 0.004

Suspended growth culture Suspended growth culture Suspended growth culture Suspended growth culture Attached growth culture Attached growth culture Attached growth culture Attached growth culture Attached growth culture Literature* Literature* Literature*

Rittmann and Manem (1992) and Rittmann and McCarty (2001)..

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all the suspended biomass washes away (at HRT 3 h affected this). About 16 runs were conducted at DO of 2.5–3.5 mg/L and N0, N and NH4+–N (influent and effluent) were observed experimentally. From the observed data, J has been computed using Eq. (19), (20) for NH4+–N. Fig. 4 shows a plot between N and J. From the plot, it is observed that J approaches zero when N approaches 0.23 mg NH4+–N/L. This suggests that the biofilm will be ineffective when the substrate concentration is less than 0.23 mg NH4+–N/L. Nmin can be represented in terms of bt, KN, Y and k as Nmin = (KN/ [(Yk/bt)  1]) and bt = Kd + bs (Rittmann, 1982a,b). On substituting the kinetic parameters in the expressions for Nmin, bt and bs were obtained as 0.19 and 0.15 d1 for NH4+–N respectively. Parameters Dw, Df were selected from literature (Rittmann and Manem, 1992; Stewart, 1998) for the present analysis. The values used in this study were Dw = 1.3 cm2/d and Df = 1.04 cm2/d. For completely mixed condition, the thickness of the stagnant layer was taken as 0.004 cm for NH4+–N (Rittmann and McCarty, 2001). The parameter Xf was estimated from experimental values for biofilm volume and weight. The average value of Xf as computed in the present case is about 9800 mg/L and for the case of nitrification, 5% of the total biomass was assumed to be comprising of nitrifiers. The kinetic parameters of the wastewater used in the present study for the model validation purpose are shown in Table 3. 7. Validation of the model developed Validation is a process of ascertaining that a model is a correct representation of the process or system for which it is intended.

Ideally, validation is said to be achieved if the predictions obtained from a model agree with the observations. The AS–biofilm nitrification reactor model developed above has been validated with the experiments conducted on an aerobic hybrid system. The experiments were conducted over a wide range of influent NH4+–N and the values of effluent NH4+–N had been observed. The model predicted values of effluent NH4+–N concentration were compared with the experimental results. Fig. 5(a) shows the experimental variations of the influent NH4+–N (N0) and effluent NH4+–N (N). Simulations were carried out by keeping all influent variables constant at their corresponding daily-mean value.

Table 4 Statistical indices describing the agreement of model and experimental results for NH4+–N. No.

Parameter

Unit

Observed

Predicted

1 2 3 4 5 6 7

Mean Standard deviation Determination coefficient (R2) Index of agreement (d) Root mean squared error (RMSE) Fraction of two (FA2) Parameters of least-squares regression C M Ratio of means (Rm)

mg/L mg/L

4.73 6.7

– mg/L –

6.3 6.2 0.78 0.76 3.52 1

mg/L – –

2.47 0.8 0.3

8

–

Fig. 5. (a) Influent and effluent profiles for NH4+–N on AS–biofilm system. (b) Simulated and experimental profiles for the effluent NH4+–N.

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Fig. 5(b) shows the experimentally obtained and simulated effluent ammonical nitrogen for the corresponding influents. The simulated ammonium concentration in the reactor is higher (mean 6.29 mg NH4+–N/L) than the measured ammonium concentration (mean 4.73 mg NH4+–N/L). According to calculations, the simulation results and the experimental results were almost consistent. The statistical indicators (Elías et al., 2006; Willmott,1981) R2, d, RMSE, FA2, C, m, and Rm calculated on the predicted and observed data sets over NH4+–N balance are shown in Table 4. It was seen that the model was able to explain 79% of the overall variability of the data (R2 = 0.79). The high value of the index of agreement (d = 0.76) showed the good agreement between observations and predictions. In all the cases, the ratio between the observed and predicted values fell within the range [0.5–2] (FA2 = 1), which meant that the errors kept below a factor of 2. The value of RMSE was low (3.52) in comparison with the typical operation values for removal efficiency. Graphical representation of the observed and predicted values in Fig. 6(a) shows that the model tends to under-predict high removal efficiency values, whilst a slight tendency towards over-prediction of low removal efficiency values. This was in agreement with the values of the regression line (C = 2.477 and m = 0.807). The value

of Rm equal to 0.3 indicates that the model can estimate the overall mean value of the observed data with acceptable accuracy. Fig. 6(b) shows the fractional error plot for the NH4+–N data sets. From the chart, it is seen that most of the error points fall within the 95% confidence limits and thus it can be said that the difference between observed and predicted data sets are insignificant at 5% level of probability for NH4+–N. 8. Conclusion An AS–biofilm model has been developed using Fouad and Bhargava (2005) explicit substrate flux expressions. This model has been solved numerically and thus obviates the need of graphical procedures inherent in the prevailing design practices. The model predictions have been compared with laboratory data and found in good agreement. Acknowledgements The Authors greatly acknowledge the French Embassy in India and INRA-LBE for providing the financial and technical help

100 90

NH4 +-N (% Remoavl)

80

70 60 50

Experimental Model

40 30

20 10 0 0

5

10

15 Cases (a)

20

25

30

Fractional Error NH4 +-N

95%UL 95%LL

95% Confidence Interval

-0.8

-0.6

-0.4

-0.2

0 0.2 Fractional Error (b)

0.4

0.6

0.8

1

Fig. 6. (a) Observed and simulated percent removal of NH4+–N. (b) Fractional error plot for NH4+–N.

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