inactivation of indicator bacte Nieznany

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Inactivation of indicator bacteria in wastewater by chlorineÐa

kinetics study

Abdennaceur Hassen

a,*

, Abderrahim Heyouni

b

, Hedi Shayeb

b

, Mohamed Cherif

c

,

Abdellatif Boudabous

d

a

Institut National de Recherche Scienti®que et Technique, Laboratoire Environnement, B.P. 24-1082, Cite Mahrajene, Tunis, Tunisia

b

Ecole Nationale des Ingenieurs de Tunis, Campus Universitaire, B.P. 37-1002, Tunis Belvederes Tunis, Tunisia

c

Institut National Agronomique de Tunisie, 43 Avenue Charles Nicole, 1082, Cite Mahrajene, Tunis, Tunisia

d

Faculte des Sciences de Tunis, Laboratoire de Microbiologie, Campus Universitaire, 1060 Tunis, Tunisia

Received 28 February 1998; received in revised form 28 April 1999; accepted 25 May 1999

Abstract

The aim of this study was to characterise the kinetics of chlorine consumption and of inactivation of indicator bacteria in

secondary wastewater using a batch laboratory reactor. In this time-course study, di€erent concentrations of chlorine, used as

NaOCl, were injected into the reactor, the levels of the di€erent forms of residual chlorine were measured, and the numbers of faecal

coliforms and faecal streptococci were determined. The results of the kinetics of chlorine consumption showed that monochlor-

amines and trichloramines were the more important forms of residual chlorine as compared to free chlorine and dichloramines. The

high contents of trichloramines indicated that the reaction of chlorine with ammoniacal nitrogen was very fast and that the

transformation of chlorine into trichloramines was carried out in a time shorter than 1 min. Experimental results showed that the

application of the model of Chick-Watson in its original form was not representative of the kinetics of inactivation of faecal

coliforms and faecal streptococci. Modi®cation of this model, in considering an initial reduction just at the contact of water with

chlorine, improved the results of adjustment of the model. The same ®ndings are valid for the model of Collins-Selleck in considering

a value m imposed to the concentration of residual chlorine, since it appeared clearly that the concentration of chlorine in¯uenced

the output of disinfection more than did the time of contact. Ó 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Wastewater; Disinfection; Chlorine; Modelling; Residual chlorine; Indicator bacteria

1. Introduction

Disinfection is often a stage for the reusability of

treated wastewater. The main objective of disinfection is

to reduce sanitary risks related to the presence of

pathogens. Assessment of sanitary risks consists in in-

dexing and identifying pathogens that may be present in

such a water. Nevertheless, a serious analytical problem

may be encountered, especially when the number of

these pathogens is relatively low and their presence is

random. A growing body of evidence has indicated that

the use of indicator bacteria, which have the advantage

of being abundant and easily countable, is very useful in

the assessment of sanitary risks related to the presence

of pathogens (Wyer et al., 1997).

Water disinfection can be achieved via di€erent

means such as chlorination, ozonation and ultraviolet

radiation (Moeller and Calkins, 1980; Come and Bariou,

1980, Anonymous, 1989). Disinfection by chlorine has

gained wide acceptance commercially, probably because

of its simplicity and its moderate cost; despite the major

problem of secondary harmful products generated by

this treatment (Pourmoghaddas and Stevens, 1995;

Racaud and Rawzy, 1994; Sanchez, 1993). Disinfection

achieved by such a process is often accomplished in two

steps: a step of fast mixture and a step of contact be-

tween chlorine and water, during a suciently long time

to allow the product to play its disinfection role. The

success of the operation of disinfection depends greatly

upon the conditions prevailing during the second step.

Besides the physico-chemical quality of the treated wa-

ter, many other factors may a€ect this operation, among

which we ®nd the hydraulic functioning of the cont-

actor, the kinetics of chlorine reaction with the

components present in water and the kinetics of

bacterial inactivation.

Bioresource Technology 72 (2000) 85±93

*

Corresponding author. Tel.: +216-1-788-436; fax: +216-1-430-934.

0960-8524/00/$ - see front matter Ó 1999 Elsevier Science Ltd. All rights reserved.

PII: S 0 9 6 0 - 8 5 2 4 ( 9 9 ) 0 0 0 8 6 - 3

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In order to characterize the functioning of such a

process, we have undertaken an experimental study en-

abling modelling of the kinetics of chlorine consumption

and bacterial inactivation in secondary wastewater.

Once combined with an adequate hydrodynamic model,

the obtained kinetics would allow the construction of a

simulation model of a chlorination reactor. The goal of

this study was, therefore, to characterize the kinetics of

chlorine consumption and indicator bacterial inactiva-

tion in secondary wastewater.

2. Methods

2.1. Wastewater treatment

Chlorination assays were performed on samples of

secondary treated wastewater (trickling ®ltrate) previ-

ously sand ®ltered in a semi-industrial pilot plant. Sand

®ltration allowed an appreciable improvement of the

quality of water and resulted in a considerable lowering

of the initial demand for chlorine.

2.2. Experimental procedure

Disinfection assays: Experiments were performed in 3

l pyrex beakers each containing a magnetic stirrer ro-

tating at 500 rpm. Wastewater (2 l) was mixed with 50

ml of disinfectant (sodium hypochlorite) prepared at

´ 10 the required ®nal dose. Wastewater chlorination

was tested with concentrations varying from 6.5 to 25

mg/l. Samples (50 ml) were taken at regular intervals

varying from 2 to 40 min, and the oxidative reaction was

immediately stopped by addition of sodium thiosulphate

before residual chlorine measurement and faecal bacte-

ria enumeration. Each assay was carried out at least 4

times. In the control, 50 ml of sterile distilled water were

mixed with wastewater samples instead of the disinfec-

tant.

Residual chlorine measurement: The di€erent forms of

residual chlorine were determined by the sulphate di-

ethyl-p-phenylenediamine (DPD) method according to

Nicholson (1965). Chlorine and derived compounds re-

act with DPD to give a red colour susceptible of tit-

rimetric measuring with ammonium ferrous (II)

sulphate solution. Addition of potassium iodide (KI) as

an oxidiser, at di€erent contact times, allowed di€eren-

tiation among free chlorine and di€erent combined

forms of chlorine such as mono-, di-, and trichlor-

amines.

Enumeration of indicator bacteria: The number of

indicator bacteria was determined based on the French

standard methods of the most probable number MPN

(Rodier, 1978), and the corrected MPN tables proposed

by Man (1983) were used.

3. Results and discussion

The goal of the present investigation was to charac-

terize the kinetics of chlorine consumption and bacterial

inactivation. The rates of reduction of faecal indicator

bacteria, as a function of time of contact, in the presence

of di€erent chlorine concentrations were determined.

The rate of inactivation was associated with a concen-

tration, C, of residual free chlorine and with a time of

contact measured using as origin time t ˆ 0 corre-

sponding to the moment of chlorine injection into the

water.

3.1. Reaction of chlorine consumption

The wastewater, even when puri®ed and treated by

®ltration, contained relatively large quantities of organic

and mineral matters with a BOD

5

content varying from

15 to 30 mg O

2

/l and a COD ranging from 20 to 30 mg

O

2

/l. The content in ammoniacal nitrogen ¯uctuated

between 8 and 20 NH

3

±N mg/l according to the exper-

iments. After the initial mixture of chlorine and water,

there was competition among two types of reactions:

· Oxido-reduction with some reducing compounds that

consume a part of the injected chlorine rendering it

unavailable for the disinfection.

· Substitution that forms some compounds of addition

or of substitution mainly with ammonia to form

chloramines, which have a low bactericidal power.

Fig. 1 shows chlorine consumption where only the

results obtained for the concentrations of 6.5 and 13.6

mg/l have been represented. From Fig. 1, it appears that

for all the studied concentrations and regardless of the

time of contact:

· Monochloramines and trichloramines remained very

important as compared to free chlorine and dichlor-

amines.

· Dichloramines appeared as the lowest chlorine form,

with a concentration usually less than 10% of the in-

jected concentration.

· Trichloramines appeared as the most important form

of residual chlorine. Their levels decreased with the

time of contact, to reach their lowest levels by the

end of the experiment (20±30 min).

These results indicated that the reaction of chlorine

with ammoniacal nitrogen of the water was very rapid

and that evolution of chlorine as trichloramines took

place in less than 1 min. This result appears to agree

with those mentioned in the literature by several authors

(Soulard, 1982; Saunier, 1979; Alouini et Seux, 1987;

Adin et al., 1991). According to Adin et al. (1991), based

on kinetic constants of these reactions, the formation of

monochloramines is the most rapid. Reactions of

chloramines destruction are relatively slow and

trichloramines are only gradually hydrolysed following

their appearance in the medium.

86

A. Hassen et al. / Bioresource Technology 72 (2000) 85±93

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· The quantity of free chlorine, the main cause of

disinfection, was variable according to the injected

concentration. In contrast, it showed, on average,

a low variation in the course of time for the same

concentration of total chlorine. For instance, with

the high chlorine concentration of 20 mg/l, the level

of free chlorine was nearly constant and of the or-

der of 3.5 mg/l (Result not shown). This result

clearly indicated that after the immediate demand

of water for chlorine, conditioned by the presence

of reducing compounds as well as compounds of

addition or substitution, the free residual chlorine

remained more or less at the same level until the

end of the experiment. It appears particularly that

the content of residual free chlorine in the second-

ary wastewater always exceeded the value of 10%

of the quantity of chlorine injected at the beginning

of the experiment. This result was valid at any time

Fig. 1. Evolution of the content of residual chlorine as a function of the time of contact. Clustred error bar graphs and bars represent standard error

of mean with at least n ˆ 4.

A. Hassen et al. / Bioresource Technology 72 (2000) 85±93

87

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of contact studied and regardless of the chlorine

concentration applied.

Based on all these results, it may be concluded that

the consumption of chlorine during the process of

wastewater disinfection undergoes two steps:

· A ®rst rapid step corresponding to the consumption

of chlorine following its reaction with the reducing

compounds in water. This step, called `the immediate

satisfaction demand', seemed to be instantaneous.

· A second step, during which residual chlorine was

transformed rapidly into the free and combined chlo-

rine forms. This step concerns particularly the pro-

cess of disinfection since residual chlorine will be

available to exert its antiseptic power. It is clear that

the modelling of the kinetics of chlorine consumption

or disinfection would concern only the second step of

the reaction, which is amenable to measurement.

On the other hand, as has previously been mentioned,

combined chlorine (mono-, di- and trichloramines) ap-

peared as the most important form of residual chlorine.

So, the role of this form of residual chlorine could not be

disregarded compared with free chlorine. In fact, free

chlorine is considered as the best disinfectant, but the

role of combined chlorine in the bacterial reduction is

not negligible (Anonymous, 1989).

3.2. Kinetic study of water disinfection by chlorine

The experimental methodology adopted consisted in

measuring simultaneously residual chlorine contents

and the number of faecal bacteria. For each chlorine

concentration applied, tests were conducted at progres-

sive contact times ranging from 2 to 40 min. The three

retained chlorine concentrations (6.5, 8.6 and 13.6 mg/l)

were tested on wastewater with MPN of 6.02 ´ 10

4

to

6.02 ´ 10

5

of faecal coliforms per 100 ml and 3.16 ´ 10

4

to 5.62 ´ 10

5

of faecal streptococci per 100 ml. All results

are reported in Table 1.

The initial contents of faecal bacteria (N

0

) in waste-

water di€ered from one experiment to another (results

not shown), which was related to the quality of water

used in each experiment. The speed of faecal bacteria

reduction varied from one concentration to the other.

The higher the initial concentration of chlorine was, the

higher was the reduction of bacteria. For instance, dur-

ing the same contact time of 10 min, a reduction in faecal

streptococci of 1.63 and 3.36 logarithmic units was ob-

tained with the respective initial chlorine concentrations

of 6.5 and 13.6 mg/l. In order to ensure a sucient safety

during wastewater reuse or rejection, the number of

faecal coliforms or streptococci must be less than 10

3

bacteria per 100 ml (White, 1976). In this study, this

objective was reached after contact times of 30, 20 and 10

min following the injection of a concentration of sodium

hypochlorite of, respectively, 6.5, 8.6 and 13.6 mg/l.

3.3. Modelling of the kinetics of disinfection

It is important to note that the approach to the ki-

netics of microorganism inactivation is generally em-

Table 1

Log reductions of faecal coliforms and faecal streptococci as a function of time and chlorine concentration

Chlorine

(mg/l)

Time

(min)

Faecal coliforms

Faecal streptococci

Free

chlorine

(mg/l)

Monochlor-

amines (mg/l)

Dichlor-

amines (mg/l)

Trichlor-

amines (mg/l)

(N/N

0

)

Reduction

a

(N/N

0

)

Reduction

6.5

2

0.0339

1.47

0.1185

0.92

1.62 ‹ 0.37

3.45 ‹ 0.38

0.97 ‹ 0.20

4.10 ‹ 0.88

5

0.0324

1.49

0.0372

1.43

1.22 ‹ 0.26

1.77 ‹ 0.32

1.07 ‹ 0.48

1.90 ‹ 0.54

10

0.0234

1.63

0.0234

1.63

1.25 ‹ 0.15

2.52 ‹ 0.24

0.47 ‹ 0.05

2.10 ‹ 0.40

20

0.0100

2.00

0.0135

1.87

1.35 ‹ 0.15

2.47 ‹ 0.85

0.52 ‹ 0.12

2.40 ‹ 1.20

30

0.0018

2.75

0.0020

2.69

1.40 ‹ 0.12

1.92 ‹ 0.42

0.67 ‹ 0.14

0.93 ‹ 0.22

40

0.0009

3.04

0.0005

3.27

1.40 ‹ 0.12

ND

ND

ND

8.6

2

0.0170

1.76

0.1632

0.78

2.68 ‹ 0.69

5.62 ‹ 0.99

1.55 ‹ 0.60

9.60 ‹ 0.70

5

0.0174

1.75

0.0724

1.32

1.72 ‹ 0.28

4.70 ‹ 1.14

1.78 ‹ 0.58

6.40 ‹ 2.50

10

0.0022

2.65

0.0100

2.00

3.30 ‹ 0.97

4.45 ‹ 1.02

0.95 ‹ 0.52

6.46 ‹ 0.60

20

0.0018

2.74

0.0052

2.28

1.52 ‹ 0.22

4.87 ‹ 0.28

0.72 ‹ 0.23

4.00 ‹ 1.86

30

0.0005

3.28

0.0007

3.12

2.97 ‹ 0.70

2.32 ‹ 1.16

0.60 ‹ 0.18

0.35 ‹ 0.04

40

0.0005

3.28

0.0007

4.12

2.52 ‹ 0.42

ND

ND

ND

13.6

2

0.01000

2.00

0.0575

1.24

2.48 ‹ 0.34

10.15 ‹ 0.30

0.60 ‹ 0.17

12.00 ‹ 3.20

5

0.00120

2.92

0.0087

2.06

3.15 ‹ 0.25

7.65 ‹ 1.04

1.88 ‹ 1.04

18.00 ‹ 1.97

10

0.00091

3.04

0.0004

3.36

4.62 ‹ 1.04

5.80 ‹ 1.20

0.68 ‹ 0.35

8.60 ‹ 1.80

20

0.00038

3.41

0.00004

4.36

3.50 ‹ 0.28

6.35 ‹ 0.28

1.62 ‹ 0.36

8.20 ‹ 2.30

30

0.00034

3.45

0.00014

3.84

1.22 ‹ 0.05

7.48 ‹ 0.58

1.08 ‹ 0.32

10.30 ‹ 1.00

40

0.00019

3.70

0.00004

4.36

1.72 ‹ 0.24

ND

ND

ND

a

Logarithmic units ˆ ÿlog (N/N

0

); N: Number of micro-organisms at the instant t; N

0

: Number of micro-organisms at the instant t ˆ 0; ‹: Standard

error.

88

A. Hassen et al. / Bioresource Technology 72 (2000) 85±93

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pirical, based on laboratory studies, and consequently a

model is only valid in conditions similar to those of its

establishment. So, concentration-time (CT) values ex-

pressed in mg.min/l were calculated by mathematical

integration of the concentration of residual free chlorine

in water versus time. In this paper only results of the

models of Chick-Watson and Collins-Selleck will be

considered as a reference and the whole results obtained

with the di€erent concentrations of chlorine will be

combined in order to establish an expression for the

kinetics of disinfection.

3.4. Chick-Watson model

The expression of the kinetics of disinfection ac-

cording to the model of Chick-Watson is given as fol-

lows: dN=dt ˆ ÿ KC

n

N with N is the number of

microorganisms, C the concentration of residual free

chlorine, n the coecient of dilution, which is a function

of the quality of water, and K is the coecient trans-

lating the disinfecting power.

Parameters to identify are K and n. By using the in-

tegrated form of the model and by changing to the

logarithm:

ln



ÿ ln

N

N

0





ˆ ln K

… † ‡ n ln C

… † ‡ ln T

… †;

and with the help of a linear regression, we can deter-

mine the values of K and n.

In this way, expressions obtained for the rate of

inactivation were

for faecal coliforms:

N

N

0

ˆ exp

ÿ

ÿ 0:1046 C

1:1

T



with a coecient of determination R

2

of 0.12.

for faecal streptococci:

N

N

0

ˆ exp

ÿ

ÿ 0:1635 C

0:7

T



with a coecient of determination R

2

of 0.42.

An illustration of these adjustments is given in Fig. 2.

Fig. 2 shows an important variation between the

measured and the calculated values. Consequently, the

model of Chick-Watson was not representative of the

kinetics of disinfection. Therefore, a second approach to

modelling was adopted and an initial microbial reduc-

tion, just at the moment of contact of water with chlo-

rine, was considered. The model becomes in this case:

N=N

0

…

† ˆ A exp ÿKC

n

T

…

† with A is the initial reduction

just at the moment of contact of water with chlorine,

The expressions obtained for the rate of reduction

were:

for faecal coliforms:

N

N

0

ˆ 0:011 exp

ÿ

ÿ 0:0369 C

1:1

T



with a coecient of determination R

2

of 0.63.

for faecal streptococci:

N

N

0

ˆ 0:0727 exp

ÿ

ÿ 0:1065 C

0:7

T



Fig. 2. Determination of the kinetic of disinfection of faecal coliforms and faecal streptococci according to the model of Chick-Watson. N: Number

of micro-organisms at the instant t; N

0

: Number of micro-organisms at the instant t ˆ 0; C: Free chlorine concentration; n ˆ parameter n of the

model; T: Time; x ˆ C

n

T ; Symbols, measured; lines, calculated.

A. Hassen et al. / Bioresource Technology 72 (2000) 85±93

89

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with a coecient of determination R

2

of 0.78. An il-

lustration of these adjustments are given in Fig. 3.

Considering,

 ˆ



X

N

N

0





cal

ÿ

N

N

0





exp

"

#

2

v

u

u

t

;

which is a parameter representative of the deviation

among calculated and measured values, the couples of

values of  before (

0

) and after (

m

) modi®cation of the

model (

0

ˆ 1.2250; 

m

ˆ 0:0393) and (

0

ˆ 0.9200;



m

ˆ 0:1319), obtained, respectively for faecal coliforms

and faecal streptococci, indicated that the modi®ed

model of Chick-Watson

N=N

0

…

† ˆ A exp ÿKC

n

T

…

†

‰

Š

better described the kinetics of bacterial disinfection

than

did

the

original

form

of

the

model

N=N

0

…

† ˆ exp ÿKC

n

T

…

†

‰

Š.

This ®nding is also con®rmed by Fig. 3 which indi-

cates that the modi®ed model of Chick-Watson de-

scribes the kinetics of bacterial disinfection when an

initial reduction was considered.

3.5. Model of Collins-Selleck

The same procedure was applied for the model of

Collins-Selleck. Parameters of identi®cation of this

model are s and n with

N

N

0

ˆ 1 for CT 6 s;

N

N

0

ˆ

s

CT





n

for CT P s:

By exploiting all experimental points, and by changing

to the logarithmic form (ln N=N

0

…

† ˆ n ln s

… † ÿ n

ln CT

…

†), the values of s and n were determined using a

linear adjustment.

The obtained expressions were:

For faecal coliforms:

N

N

0

ˆ 1 for CT 6 0:2028;

N

N

0

ˆ

0:2028

CT





1:2664

for CT P 0:2028 with r

2

ˆ 0:69:

For faecal streptococci:

N

N

0

ˆ 1 for CT 6 1:9068;

N

N

0

ˆ

1:9068

CT





2:276

for CT P 1:9068 with r

2

ˆ 0:80:

The model of Collins-Selleck has been used by Qualls

and Johnson (1985) and Montgommery (1985) for dif-

ferent kinds of wastewater. In those studies, chlorine

and dioxide of chlorine were used as disinfectants. These

authors reported s ˆ 4:06 and n ˆ 2.82 for faecal coli-

forms. These values are very di€erent from those ob-

tained in our study (s ˆ 0:2028 and n ˆ 1.266), which

Fig. 3. Determination of the kinetic of inactivation of faecal coliforms and faecal streptococci according to the model of Chick-Watson with an

initial reduction just at the moment of contact of water with chlorine. N: Number of micro-organisms at the instant t; N

0

: Number of micro-or-

ganisms at the instant t ˆ 0; C: Free chlorine concentration; n ˆ parameter n of the model; T: Time; x ˆ C

n

T. Symbols, measured; lines, calculated.

90

A. Hassen et al. / Bioresource Technology 72 (2000) 85±93

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may be explained by the quality of the water and the

operating conditions.

Fig. 4 shows rather large discrepancy between the

measured and the theoretical values for faecal coliforms,

indicating that the model of Collins-Selleck was not

representative of the obtained experimental results.

In order to improve the representativeness of this

model, a value m was imposed on the concentration of

residual chlorine, since it appeared clearly from the Figs.

2±4 that the concentration of chlorine in¯uenced the

output of disinfection more than did the time of contact.

Indeed, for a ®xed contact time, the reduction of faecal

coliforms and faecal streptococci was as great as the

concentration of applied chlorine was high. By contrast,

for a ®xed chlorine concentration, bacterial reduction

progressed relatively slowly as a function of the time of

contact.

The model becomes in this case:

N

N

0

ˆ 1 for CT 6 s;

N

N

0

ˆ

s

C

m

T





n

for CT P s:

and the parameters to be identi®ed are s, n and m.

By changing to the logarithm:

ln

N

N

0





ˆ n ln s

… † ÿ nm ln C

… † ÿ n ln T

… †;

the values of n, m and s were determined using a linear

regression. The expressions obtained were:

For faecal coliforms:

N

N

0

ˆ 1 for C

1:8

T 6 0:2484;

N

N

0

ˆ

0:2484

C

1:8

T





1:1775

for C

1:8

T P 0:2484 with r

2

ˆ 0:74:

For faecal streptococci:

N

N

0

ˆ 1 for CT 6 1:5783;

N

N

0

ˆ

1:5783

C

0:68

T





2:3091

for CT P 1:5783 with r

2

ˆ 0:80:

Fig. 5 indicates, particularly for faecal coliforms, that

the model of Collins-Selleck in the modi®ed form:

N=N

0

ˆ s=C

m

T

…

†

n

allows a better description of the ki-

netics of decontamination than does its original form:

N=N

0

ˆ s=CT

…

†

n

:

Indeed, when we calculated the deviation

 ˆ



X

N=N

0

…

†

cal

ÿ N=N

0

…

†

exp

h

i

2

r

for the two models, the values obtained according to the

modi®ed form of the model of Collins-Selleck were

lower than those corresponding to the original form of

the same model (Table 2). Also, the di€erent expressions

obtained according to the kinetic approaches of both

Chick-Watson and Collins-Selleck are reported in

Table 2.

Fig. 4. Determination of the kinetic of disinfection of faecal coliforms and faecal streptococci according to the model of Collins-Selleck. N: Number

of micro-organisms at the instant t; N

0

: Number of micro-organisms at the instant t ˆ 0; C: Free chlorine concentration; m ˆ parameter m of the

model; T: Time. Symbols, measured; lines, calculated.

A. Hassen et al. / Bioresource Technology 72 (2000) 85±93

91

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4. Conclusions

The following conclusions may be drawn from the

present kinetics study:

· Monochloramines and trichloramines appeared as

the most important residual chlorine forms as com-

pared to free chlorine and dichloramines.

· The high levels of trichloramines showed clearly that

the reaction of chlorine with ammoniacal nitrogen is

very fast and that evolution of chlorine into trichlor-

amines is carried out in a time shorter than 1 min.

· The original model of Chick-Watson ln N=N

0

…

† ˆ

ÿKC

n

T was not able to describe the inactivation ki-

netics of indicator bacteria. Therefore, a modi®ca-

tion, based on the same model but after taking into

consideration an initial inactivation during the con-

tact

of

water

with

chlorine

ln N=N

0

…

† ˆ

A exp ÿKC

n

T

…

†, described very well the kinetics of

disinfection of faecal coliforms and faecal strep-

tococci.

· The same remarks were valid for the model of Col-

lins-Selleck, which, in modi®ed form, N=N

0

ˆ

s=C

m

T

…

†

n

described the kinetics of disinfection better

than did the original form.

Acknowledgements

This investigation was supported by grants from the

International Foundation for Science (H-2327, IFS,

Sweden) and from the CEE (Avicenne No. 93 AVI 054).

We thank Professor Jean J. Damelincourt, Centre de

Fig. 5. Determination of the kinetic of disinfection of faecal coliforms and faecal streptococci according to the modi®ed model of Collins-Selleck. N:

Number of micro-organisms at the instant t; N

0

: Number of micro-organisms at the instant t ˆ 0; C: Free chlorine concentration; m ˆ parameter m of

the model; T: Time; x ˆ C

m

T . Symbols, measured; lines, calculated.

Table 2

Expressions obtained according to the kinetic models studied

a

Bacteria

Model

Expression

R

2



FC

Chick-Watson

N

N

0

ˆ exp…ÿ0:1046C T †

0.12

1.2250

Chick-Watson modi®ed

N

N

0

ˆ 0:011 exp…ÿ0:0269C

1:1

T †

0.63

0.0393

Collins-Selleck

N

N

0

ˆ

0:2028

C T

ÿ



1:2664

0.69

0.0327

Collins-Selleck modi®ed

N

N

0

ˆ

0:2484

C

1:8

T

ÿ



1:1775

0.74

0.0248

FS

Chick-Watson

N

N

0

ˆ exp…ÿ0:1635C

0:7

T †

0.42

0.9200

Chick-Watson modi®ed

N

N

0

ˆ 0:0727 exp…ÿ0:106C

0:7

T †

0.78

0.1319

Collins-Selleck

N

N

0

ˆ

1:9068

C T

ÿ



2:276

0.80

0.2227

Collins-Selleck modi®ed

N

N

0

ˆ

1:5738

C

0:68

T

ÿ



2:3091

0.80

0.1900

a

FC: Faecal coliforms, FS: Faecal streptococci, R

2

: Coecient of determination, : Deviation among calculated and measured values, N: Number of

micro-organisms at the instant t; N

0

: Number of micro-organisms at the instant t ˆ 0; C: Free chlorine concentration; T: Time.

92

A. Hassen et al. / Bioresource Technology 72 (2000) 85±93

background image

Physique des Plasmas et Applications de Toulouse,

University Paul Sabatier, France, for his help.

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93


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