Reactions between aqueous chlorine and ammonia : a predictive … · 2019. 2. 13. · Abstract The...

Reactions between Aqueous Chlorine and Ammonia: A Predictive Model

A Dissertation Presented

by

Xin (Cindy) Huang

to

The Department of Civil and Environmental Engineering

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in

Civil Engineering

Northeastern University Boston, Massachusetts

(July, 2008)

Abstract

The Unified Plus Model was proposed in this study as a predictive tool for reactions

between aqueous chlorine and ammonia. Based on the Unified Model (Jafvert 1985), the

reaction scheme was changed by removal of Reaction 10 and inclusion of trichloramine

hydrolysis reaction. The rate coefficient for monochloramine formation was re-evaluated

to incorporate the latest reported values (Qiang and Adams 2004). To ensure the user-

friendly nature of a mechanistic based model, Visual Basic for Application was used as

the programming language and Excel was used as the interface.

The Unified Plus Model was calibrated and validated to the following ranges of initial

conditions, pH 6.5 – 9.5, temperature 4 – 30°C, total carbonate buffer concentration

9x10-4 – 1x10-2 M, and initial chlorine to ammonia molar ratio (Cl2/N)0 0.5 to 2.0. It can

reasonably predict chloramine species concentrations in synthetic solution using the

initial conditions within the above ranges.

The potential applications of the Unified Plus Model were demonstrated through case

studies. With some moderate modifications, the model can be used to generate breakpoint

curves, which can demonstrate the effect of open system as well as degree of mixing on

the speciation of chloramine species. This model was also used to successfully reproduce

the observed breakpoint phenomenon during switching between monochloramine and

chlorine. An attempt was made to incorporate the effect of NOM (Duirk, 2005) and to

simulate disinfectant loss in a full scale system.

Acknowledgements

Life is a journey of self-improvement. I am forever grateful for those who guided me,

supported me, cheered for me, and accompanied me. In particular, Dr. Irvine W. Wei, my

long time advisor, has always been there to answer my questions, clear my doubts, and

encourage me. He not only taught me how to conduct research, but also how to be a

better person in life, which I will always cherish. Dr. Ferdi Hellweger offered tremendous

help on the modeling aspect, which is essential to this study. Dr. Windsor Sung provided

a unique perspective and invaluable input as a scientist working in the drinking water

industry. Dr. Russell Isaac’s immense knowledge on chloramine chemistry and water

quality modeling was also invaluable.

I would also like to thank the Department of Civil and Environmental Engineering at

Northeastern University for the financial support and my friends there for their emotional

support throughout the years. Without the caring staff and fellow graduate students, this

journey would have been much less fulfilling.

I also thank Dr. Richard Valentine and Dr. Chad Jafvert for their help and willingness to

share their knowledge on the Unified Model.

Finally, I would like to express my deepest gratitude to my beloved parents, Xueying

Chen and Yanling Huang. Thank you for bringing me up as who I am.

i

Table of Contents Table of Contents ................................................................................................................. i

List of Figures .................................................................................................................... iii

List of Tables ..................................................................................................................... vi

1 Introduction and Objectives ........................................................................................ 1

1.1 Current practice and future of chloramination .................................................... 1

1.2 Existing models of aqueous chlorine and ammonia ........................................... 3

1.3 Objectives ........................................................................................................... 5

2 Literature Review ........................................................................................................ 6

2.1 The reaction scheme of the Unified Model ......................................................... 6

2.2 Rate coefficients of the Unified Model ............................................................... 8

2.2.1 Specific rate coefficient of monochloramine formation reaction ............... 8

2.2.2 Rate coefficient for other reactions ........................................................... 21

2.3 Trichloramine hydrolysis reaction .................................................................... 31

3 Model Setup .............................................................................................................. 34

3.1 Model implementation using Visual Basic for Application (VBA) ................. 35

3.2 Sensitivity analysis............................................................................................ 36

4 Data Collection ......................................................................................................... 43

4.1 Available data from the literature ..................................................................... 43

4.2 Experimental procedures and methods ............................................................. 44

5 Model Calibration and Validation ............................................................................ 48

5.1 Calibration......................................................................................................... 51

5.1.1 Calibration in the combined chlorine region ............................................ 52

ii

5.1.2 Calibration in breakpoint region ............................................................... 66

5.2 Validation .......................................................................................................... 75

6 Case Studies .............................................................................................................. 78

6.1 Breakpoint curve ............................................................................................... 78

6.2 Mixing effect ..................................................................................................... 82

6.3 Open system ...................................................................................................... 86

6.4 Switching disinfectant ....................................................................................... 92

6.5 Natural Organic Matter (NOM) ........................................................................ 97

7 Conclusions and Recommendations ....................................................................... 105

References ....................................................................................................................... 109

Appendix A Recalculated Values of k1 for Correlation Analysis .................................. 114

Appendix B Initial Conditions of Available Data from the Literature ........................... 117

Appendix C Experimental Data ...................................................................................... 119

Appendix D Initial Conditions and Results of Sensitivity Analysis ............................... 122

Appendix E Source Code ................................................................................................ 135

Appendix F Comparison between Model Simulation and Palin’s Data ......................... 147

iii

List of Figures

Figure 2-1 Correlation of k1 and ionic strength at different initial (Cl2/N)0 , T=25°C .... 18 Figure 2-2 Correlation of k1 and (Cl2/N)0 at different ionic strength, T=25°C ................ 19 Figure 2-3 k1 as a function of temperature from different sources .................................. 20 Figure 2-4 Specific rate constant of k1 as a function of temperature ............................... 20 Figure 2-5 Linear Free Energy Relationship (Bronsted Plot) ........................................... 25 Figure 3-1 Sensitivity of monochloramine to all reaction coefficients at 6 hours ............ 38 Figure 5-1 Comparison between model simulation and data (Data source Valentine 1998

Fig 4.1) .................................................................................................................. 53 Figure 5-2 Comparison between model simulation and data (Data source Valentine 1998



Fig4.1) ................................................................................................................... 54 Figure 5-5 Comparison between model simulation and data (Data source Valentine 1998














Fig4.7) ................................................................................................................... 61

iv

Figure 5-19 Comparison between model simulation and data (Data source Valentine 1998 Fig4.7) ................................................................................................................... 62




Figure 5-23 Comparison between model simulation and data (Data source Valentine 1998 Fig4.10) ................................................................................................................. 64

Figure 5-24 Comparison between model simulation and data from Exp1 ....................... 64 Figure 5-25 Comparison between model simulation and data from Exp2 ....................... 65 Figure 5-26 Comparison between model simulation and data from Exp3 ....................... 65 Figure 5-27 Comparison between model simulation and data from Exp4 ....................... 70 Figure 5-28 Comparison between model simulation and data from Exp5 ....................... 70 Figure 5-29 Comparison between model simulation and data from Wei Exp 4-25 ......... 71 Figure 5-30 Comparison between model simulation and data from Wei Exp 4-26 ......... 71 Figure 5-31 Comparison between model simulation and data from Wei Exp 4-27 ......... 72 Figure 5-32 Comparison between model simulation and data from Wei 1972 on the

impact of initial ammonia concentration on dichloramine concentration ............ 73 Figure 5-33 Model simulated formation of nitrate as a fraction of initial ammonia at

different (Cl2/N)0 at 1 hour .................................................................................... 74 Figure 5-34 Model simulated formation of trichloramine as a fraction of initial ammonia

at different (Cl2/N)0 at 1 hours .............................................................................. 74 Figure 5-35 Comparison between model simulation and data from Exp6 ....................... 76 Figure 6-1 Simulated breakpoint curve after 45 minutes at initial pH 9 .......................... 80 Figure 6-2 Simulated breakpoint curve after 45 minutes at initial pH 8 .......................... 81 Figure 6-3 Simulated breakpoint curve after 45 minutes at , initial pH 7 ........................ 81 Figure 6-4 Simulated breakpoint curve after 45 minutes at initial pH 6 .......................... 82 Figure 6-5 Breakpoint curve of total chlorine concentration (Data source: Jain 2007) .... 83 Figure 6-6 Comparison between simulated breakpoint curve and data (Data source: Jain

2007) ..................................................................................................................... 85 Figure 6-7 The impact of open system on monochloramine stability 25°C, pH 8.31, µ

0.1M, CTCO3 0.004M, (Cl2/N)0 0.5 ....................................................................... 89 Figure 6-8 The impact of open system on pH 25°C, pH 8.31, µ 0.1M, CTCO3 0.004M,

(Cl2/N)0 0.5 ........................................................................................................... 89 Figure 6-9 Impact of open system on monochloramine stability 25°C, pH 6.55, µ 0.05M,

CTCO3 0.004M, (Cl2/N)0 0.7 .................................................................................. 90 Figure 6-10 Impact of open system on pH 25°C, pH 6.55, µ 0.05M, CTCO3 0.004M,

(Cl2/N)0 0.7 ........................................................................................................... 90 Figure 6-11 Impact of open system on monochloramine stability Exp2 22°C, pH 9.57, µ

0.01M, CTCO3 0.0009M, (Cl2/N)0 0.9 ................................................................... 91 Figure 6-12 Impact of open system on pH 22°C, pH 9.57, µ 0.01M, CTCO3 0.0009M,

(Cl2/N)0 0.9 Exp2 ................................................................................................. 91 Figure 6-13 Breakpoint phenomenon observed during the switch from chloramine to free

chlorine (Ferguson, DiGiano et al. 2005) ............................................................ 93

v

Figure 6-14 Breakpoint phenomenon observed during the switch from free chlorine to chloramine (Ferguson, DiGiano et al. 2005) ....................................................... 93

Figure 6-15 Breakpoint phenomenon during switch from chloramine to chlorine simulated by Unified Plus Model 3.4 mg/L monochloramine to 1.5 mg/L free chlorine, 10°C, pH 8 ............................................................................................. 96

Figure 6-16 Breakpoint phenomenon during switch from free chlorine to monochloramine simulated by Unified Plus Model 1.5 mg/L free chlorine to 3.4 mg/L monochloramine, 10°C, pH 8 ...................................................................... 97

Figure 6-17 Raw water UV254 absorbance and water temperature at the end of the clear well in MWRA system ........................................................................................ 100

Figure 6-18 Comparison between model simulation and full scale data on the week of June 11, 2007 Raw water UV254 0.09 13.6°C ................................................... 102

Figure 6-19 Comparison between model simulation and full scale data on the week of June 25, 2007 Raw water UV254 0.086 14.7°C ................................................. 102

Figure 6-20 Comparison between model simulation and full scale data on the week of July 2, 2007 Raw water UV254 0.083 15.3°C .................................................... 103

Figure 6-21 Comparison between model simulation and full scale data on the week of July 9, 2007 Raw water UV254 0.079 14.3°C .................................................... 103

Figure 6-22 Comparison between model simulation and full scale data on the week of July 16, 2007 Raw water UV254 0.075 16.1°C ................................................... 104

Figure 6-23 Comparison between model simulation and full scale data on the week of June 19, 2006 Raw water UV254 0.09 14.3°C .................................................... 104

vi

List of Tables

Table 1-1 Typical Ranges of Parameters for Chloramination Process ............................... 2 Table 2-1 Reaction Scheme of the Unified Model (Jafvert and Valentine 1992) .............. 7 Table 2-2 Reported Values of the Specific Rate Coefficient of Monochloramine

Formation ................................................................................................................ 8 Table 2-3 Experimental Conditions for Monochloramine Formation Reaction ............... 13 Table 2-4 Reaction Scheme and Rate Coefficients for the Unified Plus Model .............. 33 Table 5-1 Updated Reaction Scheme and Rate Coefficients for the Unified Plus Model 50 Table 5-2 Final Reaction Scheme and Rate Coefficients for the Unified Plus Model ..... 77 Table 6-1 Initial Condition Used for Simulation of Switching Disinfectant .................... 95 Table A-1 Recalculated Values of k1 for Correlation Analysis ..................................... 115 Table B-1 Initial Conditions of Available Data from the Literature .............................. 118 Table C-1 Experimental Conditions ............................................................................... 120 Table C-2 Experimental Results ..................................................................................... 120 Table D-1 Initial Condition Used for Sensitivity Analysis of the Unified Plus Model .. 123 Table D-2 Calculated Condition Numbers for Monochloramine ................................... 125 Table D-3 Calculated Condition Numbers for Dichloramine ......................................... 127 Table D-4 Calculated Condition Numbers for Free Chlorine ......................................... 129 Table D-5 Calculated Condition Numbers for Trichloramine ........................................ 131 Table D-6 Calculated Condition Numbers for pH .......................................................... 133

1

1 Introduction and Objectives

1.1 Current practice and future of chloramination

Chloramines are a group of chemicals including monochloramine, dichloramine, and

trichloramine. They are formed when aqueous chlorine and ammonia are mixed at

different molar ratios (Cl2/N)0. Chloramination is a disinfection process in drinking water

treatment, during which aqueous chlorine and ammonia are added to water and produce

chloramines. For disinfection purpose, monochloramine is the most desirable species

among the three due to its chemical stability and biocidal property.

Chloramination was first introduced as a drinking water disinfection process in the

1920’s (McGuire 2006). Later in the 1940’s, breakpoint chlorine reactions were

discovered and used to destroy ammonia in natural water or wastewater and to achieve

disinfection by the residual free chlorine (McGuire 2006). Often used as secondary

disinfection, chloramination, if optimized, will produce monochloramine. Compared with

free chlorine, monochloramine is less reactive and consequently leads to less Disinfection

By-Products (DBPs), specifically Total Trihalomethanes (TTHM), and more stable

residual disinfectant in the distribution system (Kirmeyer, Martel et al. 2004). However,

if chloramination process is not optimized, problems can occur, such as unstable

disinfectant residual, high total coliform, nitrification and high nitrate concentration in

the distribution system (Harrington, Noguera et al. 2003; Kirmeyer, Martel et al. 2004;

Seidel, McGuire et al. 2005). Inadequate understanding of chloramine chemistry and

difficulty in process control are often the causes of these problems. In a 2004 American

Water Works Association Research Foundation (AWWARF) report, the optimal ranges

for some of the key parameters were suggested, within which were pH 8 to 9, and

2

chlorine to ammonia nitrogen weight ratio 4:1 to 5:1 ((Cl2/N)0 0.8 – 1) (Kirmeyer, Martel

et al. 2004). Nevertheless these ranges are not always practiced in reality. As seen in

Table 1-1, the typical ranges of parameters used during chloramination were summarized

from survey responses of 68 utilities (Kirmeyer, Martel et al. 2004).

Table 1-1 Typical Ranges of Parameters for Chloramination Process Parameters Ranges pH 6.2 – 10.5 Temperature 0 – 36 °C Residual concentration 0 – 6.8 mg/L as Cl2 Alkalinity 10 – 340 mg/L as CaCO3 Chlorine to ammonia nitrogen weight ratio 3 – 7

In 1998, 30% of large utilities used chloramines. This percentage had not changed much

since (McGuire 2006). A survey on the secondary disinfection practices was conducted in

2005 (Seidel, McGuire et al. 2005). The result showed that surface water systems were

more likely to use chloramine than groundwater systems while large systems were more

likely to use chloramine than small systems. Out of the 363 surveyed utilities, 3% were in

the process of converting and another 12% were considering changing from chlorine to

chloramine. The Stage 2 D/DBPR (Disinfectants, Disinfectant By-Product Rule)

published in January 2006, required systems to lower DBP concentration in the

distribution systems by 2017. Under these circumstances, more and more utilities are

expected to switch to chloramination (McGuire 2006). In an economic analysis for the

Rule, the US Environmental Protection Agency (USEPA) projected the future use of

chloramine to increase from 13.5% before the Stage 1 D/DBPR to 54.6% after the

compliance with the Stage 2 D/DBPR for community water systems using surface water

as their sources (Seidel, McGuire et al. 2005).

3

1.2 Existing models of aqueous chlorine and ammonia

Both mechanistic and empirical models were reported in the literature to evaluate the

formation and decay of chloramines.

The reaction mechanisms and kinetics between aqueous chlorine and ammonia have been

studied by many researchers for more than half a century (Weil and Morris 1949;

Granstrom 1954; Wei 1972; Saunier 1976; Johnson and G. W. Inman 1978; Margerum,

Gray et al. 1978; Leao 1981; Morris and Isaac 1983; Jafvert 1985; Diyamandoglu 1989;

Qiang and Adams 2004). Not only the individual reactions were studied, different

reaction schemes of this complicated reaction system were also proposed. Wei (1972)

and Saunier (1976) investigated the potential reaction scheme in the breakpoint region

((Cl2/N)0>1.5). Later Leao (1981) suggested a reaction scheme in the combined chlorine

region (0< (Cl2/N)0≤ 1). Jafvert (1985) integrated the reported reaction schemes and

formulated the Unified Model, which covered the reactions taking place in the combined,

breakpoint, as well as transition (1< (Cl2/N)0≤ 1.5) regions. This model can predict

reactions between aqueous chlorine and ammonia in phosphorus buffer system

reasonably well at 25°C (Jafvert and Valentine 1992). Valentine et al adopted those

reactions in the combined chlorine region from the Unified Model and showed a

satisfactory prediction of the decay of monochloramine in carbonate buffer system at

different temperatures (Valentine, Ozekin et al. 1998). John Woolschlager (Woolschlager

2000) modified the Unified Model and incorporated it into the Comprehensive

Disinfection and Water Quality (CDWQ) model. This model also counted

monochloramine loss due to natural organic matter (NOM), corrosion, nitrification, and

pipe surface. Since it was designed as a distribution system water quality model, the

4

implementation requires a well calibrated hydraulic model, which can be a challenging

task by itself. These mechanistic models captured the details of the reaction system yet

were not developed to be user friendly.

Unlike mechanistic models, empirical models on the other hand are straight forward and

easy to use. Scott Summers and his students reported using a regression model to predict

monochloramine demand (Work, Smith et al. 2004).

)()()( 0 UVATOCCLMCLMDt υτχ ++=

CLMDt: chloramine demand at time t, mg/L as Cl2 CLM0: chloramine dose, mg/L as Cl2 TOC: Total organic carbon concentration, mg/L UVA: ultraviolet absorbance at 254nm, cm-1 χ, τ, υ: regression coefficients, χ & τ dimensionless, υ (cm mg/L)

At each time of interest, a different set of regression coefficients have to be obtained.

This jeopardizes its usage to predict chloramine concentration as a function of time.

Wilczak used a two stage first order empirical equation to describe the “first very fast and

then slow” pattern of chloramine decay (Wilczak 2005). This model was found to

sufficiently describe chloramine decay in the distribution system of East Bay Municipal

Utility District (EBMUD). The above models are only concerned with chloramine decay

after its production and do not provide any insights on the formation reactions.

The chemistry between aqueous chlorine and ammonia is very complex and is highly pH

and temperature dependent. It is crucial to understand the chemistry in order to achieve

optimal results in practice. Unfortunately, this can not be accommodated by the empirical

models. On the other hand, the mechanistic models were usually developed in

sophisticated programming languages with inconvenient input and output format, which

hinders their practical application. As a result, the water utilities are still using the

5

qualitative guidelines instead of quantitative models during planning and daily operation,

which are subject to a series of problems as described previously.

1.3 Objectives

The goal of this study is to develop a mechanistic based model which includes the

comprehensive chemistry between aqueous chlorine and ammonia but at the same time is

easy to use, so that it can be an educational and predictive tool to water utilities at both

operator and management level or as a basis for process design for engineers.

The detailed objectives are:

1. To update the most comprehensive reaction scheme from literature and all the

associated rate coefficients.

2. To develop the model in a user friendly environment.

3. To calibrate the model using typical ranges of parameters found in field practice.

4. To demonstrate the potential use of this model through case studies.

6

2 Literature Review

2.1 The reaction scheme of the Unified Model

In his dissertation, Jafvert reviewed the reaction schemes reported by various researchers

(Wei 1972; Saunier 1976; Leao 1981) in great details and proposed a reaction scheme

which comprised of the reactions taking place in both combined and breakpoint regions.

There are 14 reactions included in the Unified Model as shown in Table 2-1. They can be

summarized into four categories (Jafvert 1985): 1) the substitution reactions including

monochloramine, dichloramine, and trichloramine formation (Reaction 1, 3, 11), and

their corresponding hydrolysis reactions (Reaction 2 and 4); 2) the disproportionation

reaction of monochloramine and the corresponding back reactions (Reaction 5 and 6); 3)

the redox reactions that occur in the absence of measurable free chlorine and presence of

free ammonia (Reaction 7, 8, and 9); 4) the redox reactions that occur when measurable

free chlorine is present (Reaction 12, 13, and 14). Reaction 11 and 12 were proposed by

Margerum (1983) and Reaction 13 and 14 were proposed by Jafvert (1985) as part of the

postulated mechanism during breakpoint reactions. Reaction 10 was postulated and

included in the reaction scheme to ensure a good fit between the experimental data and

the model (Leao 1981). Each reaction and the rate coefficient will be reviewed in detail in

the next section.

The Unified Model was calibrated to a range of experimental conditions, i.e. 25°C, pH 6

to 8, total phosphate buffer 0.01 M, initial chlorine/monochloramine concentration

1.4x10-4 to 7x10-4 M (10 to 50 mg/L as chlorine), and chlorine to ammonia molar ratio

(Cl2/N)0 0.2 to 2.0. It showed satisfactory results when compared to experimental data at

7

25°C (Jafvert and Valentine 1992). No temperature effect was considered for any of the

reaction coefficients.

Table 2-1 Reaction Scheme of the Unified Model (Jafvert and Valentine 1992)

No. Reactions Coeff. Rate Expression 1 HOCl + NH3 → NH2Cl + H2O k1 k1[HOCl][NH3] 2 NH2Cl + H2O → HOCl + NH3 k2 k2[NH2Cl] 3 HOCl + NH2Cl → NHCl2 + H2O k3 k3[HOCl][NH2Cl] 4 NHCl2 + H2O → HOCl + NH2Cl k4 k4[NHCl2] 5 NH2Cl + NH2Cl → NHCl2 + NH3 k5 k5[NH2Cl][NH2Cl] 6 NHCl2 + NH3 → NH2Cl + NH2Cl k6 k6[NHCl2][NH3][H+] 7 NHCl2 + H2O → NOHa + 2HClb k7 k7[NHCl2][OH-] 8 NOHa + NHCl2 → HOCl + N2

b + HCl b k8 k8[I][NHCl2] 9 NOHa + NH2Cl → N2

b + HCl b + H2Ob k9 k9[I][NH2Cl] 10 NH2Cl + NHCl2 → N2

b + 3HClb k10 k10[NH2Cl][NHCl2] 11 HOCl + NHCl2 → NCl3 + H2O k11 k11[HOCl][NHCl2] 12 NHCl2 + NCl3 + 2H2O → 2HOCl + N2

b + 3HClb k12 k12[NHCl2][NCl3][OH-] 13 NH2Cl + NCl3 + H2O → HOCl + N2

b + 3HClb k13 k13[NH2Cl][NCl3][OH-] 14 NHCl2 + 2HOCl + H2O → NO3

- + 5H+ + 4Cl- k14 k14[NHCl2][OCl-] a Assumed formula for the unidentified intermediate. b Products and stoichiometry are assumed for balancing the reaction. Possible products may include N2, H2O, Cl-, H+, NO3

-, and other unidentified reaction products.

Later Valentine et al (Valentine, Ozekin et al. 1998) adopted Reaction 1 to Reaction 10

and calibrated it to the following experimental conditions, (Cl2/N)0 from 0.5 to 0.7,

temperature 4 to 35°C, pH 6.6 to 8.3, ionic strength (μ) 0.005 to 0.1 M, total carbonate

buffer concentration 0.001 to 0.01 M, and initial chlorine concentration 1x10-5 to

1.06x10-4 M (0.71 to 7.53 mg/L as chlorine). The model successfully predicted

monochloramine formation and loss in the combined region over 7 days in carbonate

buffer system (Valentine, Ozekin et al. 1998).

The reaction scheme of the Unified Model, being the most comprehensive, was adopted

as the basis for this study, and was updated and calibrated to data generated in carbonate

buffer system.

8

2.2 Rate coefficients of the Unified Model

The 14 reactions and their rate coefficients listed in Table 2-1 are reviewed in this section

with the emphasis on major developments after the Unified Model was proposed.

2.2.1 Specific rate coefficient of monochloramine formation reaction

The first reaction, formation of monochloramine from mixing aqueous free chlorine and

ammonia, had been studied by various researchers (Weil and Morris 1949; Johnson and

G. W. Inman 1978; Johson and G. W. Inman 1978; Margerum, Gray et al. 1978; Morris

and Isaac 1983; Qiang and Adams 2004). The reported values of the specific rate

coefficient are summarized in Table 2-2. Despite the fact that the values are in the same

order of magnitude at 25°C, they are quite scattered. For example, the value reported by

Weil and Morris is about double of that reported by Margerum et al. This disparity, as

well as the large sensitivity of the Unified Model towards k1 (see Section 3.2) in the

combined chlorine region, necessitated a re-evaluation of k1.

Table 2-2 Reported Values of the Specific Rate Coefficient of Monochloramine Formation

Sources Temp °C

k1 at 25°C M-1s-1 Arrhenius Equation

Weil & Morris 1949 5.9 - 35 6.20E+06 2.5x1010xexp(-2500/RT) Margerum et al 1978 25 2.80E+06 N/A

Johnson & Inman 1978 25 3.10E+06 N/A Morris & Isaac 1983 3.9 - 34.1 4.20E+06 6.6x108xexp(-1510/T) Qiang & Adam 2004 5 - 35 3.07E+06 5.4x109xexp(-2237/T)

Both Johnson (1978) and Morris (Morris and Isaac 1980), speculated that the potential

cause of this difference in the reported values may be due to the difference in initial

chlorine to ammonia molar ratio (Cl2/N)0 used by Weil and others. If this was true, the

value of k1 should be expected to have some correlation with (Cl2/N)0.

9

The values reported by Morris and Isaac (1983) are the most often cited to date. During

the formulation of the Arrhenius Equation, Morris and Isaac excluded the data from

Johnson and Inman as well as those from Margerum, Gray, and Huffman, claiming that

those reported values were not applicable to fresh waters due to the high ionic strength

used in their experiments. This implies that k1 might be correlated to ionic strength.

Therefore, two questions must be answered through a thorough literature review.

1. Is k1 correlated to ionic strength?

2. Is k1 correlated to initial chlorine to ammonia molar ratio (Cl2/N)0 ?

Ionic strength correction It is agreed by all the investigators that aqueous monochloramine formation reaction is

second-order, and is first-order with respect to each reactant in the form of neutral

molecule, as shown in Equation 2-1.

ClNH

HOClNHHOClNHkdt

ClNHd

2

33

2 ]][[1][

γγγ ⋅

= Equation 2-1

k1 – specific rate coefficient, M-1s-1 [NH3] – ammonia concentration, M [HOCl] – hypochlorous acid concentration, M γ - activity coefficient of the corresponding species

For most cases during experiment and full scale operation, total free chlorine (HOCl and

OCl-) and total free ammonia (NH3 and NH4+) are measured, instead of hypochlorous

acid and ammonia. Thus the dissociation of hypochlorous acid and ammonium are

incorporated into Equation 2-1 to obtain Equation 2-4.

−+ +⇔ OClHHOCl

HOCl

OClHaHOCl HOCl

OClHK

γγγ

⋅⋅⋅

= −+−+

][]][[

Equation 2-2

10

34 NHHNH +⇔ ++

++

++

+⋅

⋅⋅=

44

334 ][

]][[

NH

NHHaNH NH

NHHK

γγγ Equation 2-3

Ka – acid dissociation constant for corresponding species, M γ - activity coefficient of the corresponding species

ClNH

HOClNHNTClT

HOClaHOClOClH

OClH

NHaNHNHH

NHaNH CCKH

HKH

Kk

dtClNHd

2

3,,

443

442

][][

][1][

γγγ

γγγγγ

γγγγ ⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+⋅⋅

⋅⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+⋅⋅

⋅=

−++

−++

+++

+

Equation 2-4

k1 – specific rate coefficient, M-1s-1 CT,Cl – total free chlorine concentration, M CT, N – total free ammonia concentration, M Ka – acid dissociation constant for corresponding species, M γ - activity coefficient of the corresponding species

In dilute aqueous solution, the activity coefficients of neutral molecules are considered to

be unity. Thus ClNHHOClNH 23 ,, γγγ are all equal to 1. All the monovalent ions have the

same activity coefficient which is calculated using the Güntelberg approximation of the

DeBye-Hückel theory (Snoeyink and Jenkins 1980),

2/1

2/12

15.0

logμμ

γ+

=− ii

Z Equation 2-5

Z – charge of the ion

µ – ionic strength

Ionic strength is one of the key experimental conditions. During full scale operation it can

be estimated empirically by using the Total Dissolved Solid (TDS) or conductivity of the

water (Snoeyink and Jenkins 1980).

After the simplification, Equation 2-4 is transformed into Equation 2-6.

NTClTaHOClaNH

aNH CCKH

HKH

Kk

dtClNHd

,,4

42

][][

][1

][⎟⎟⎠

⎞⎜⎜⎝

⎛

+⋅⋅⋅⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅+⋅⋅

=−+

+−+

+

+++

+

γγγγ

γγγ Equation 2-6

11

k1 – specific rate coefficient, M-1s-1 CT,Cl – total free chlorine concentration, M CT, N – Total free ammonia concentration, M Ka – acid dissociation constant for corresponding species, M γ - activity coefficient of the corresponding species

Since pH probe measures the activity of the hydrogen ion, in other

words, )]log([ ++ ⋅−= γHpH , Equation 2-6 can be expressed as the following.

NTClTaHOCl

pH

pH

aNHpH

aNH CCKK

Kk

dtClNHd

,,4

42

1010

101

][⎟⎟⎠

⎞⎜⎜⎝

⎛

+⋅⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅+⋅

=−

−−

−

+−

+

γγ

γγ Equation 2-7

k1 – specific rate coefficient, M-1s-1 CT,Cl – total free chlorine concentration, M CT, N – Total free ammonia concentration, M Ka – acid dissociation constant for corresponding species, M γ - activity coefficient of the corresponding species

As illustrated above, if the reaction mechanism is correct, the ionic strength should not

affect k1. Thus in the critical review of Morris (1983), the exclusion of those values

where high ionic strength was used would be questionable and k1 should have no

correlation to ionic strength.

KaHOCl and KaNH4

Among the studies reviewed, inconsistent values were used for the dissociation constants

of hypochlorous acid and ammonium. This can be a potential cause of the discrepancy in

the reported k1 values. A review on these dissociation constants was conducted.

For the dissociation constant of ammonium, this work adopted the formula reported by

Emerson and Thurston (Emerson, Russo et al. 1975). They evaluated the “best data to-

date” from Bates and Pinching (Bates and Pinching 1949) and proposed the empirical

best fit for 0 to 50°C.

12

TpKaNH /92.272909018.04 +=+ Equation 2-8

T – temperature, K

This gives the value of 9.25 at 25°C, which is the same value as reported in CRC

Handbook (Lide 2005-2006).

Morris (Morris 1966) reported the following empirical formula for hypochlorous acid in

the temperature range of 4 to 34°C.

TTpKaHOCl 0253.00686.10/00.3000 +−= Equation 2-9


At 25°C, the acid dissociation constant has a value of 7.537, and is significantly higher

than 7.40, the reported value in CRC Handbook (Lide 2005-2006). Among all the data

summarized by Perrin (Perrin 1982), which is referenced by CRC Handbook, Morris’s

1966 paper is the latest among the available journal papers in English and the only one

that provides a formula of pKa as a function of temperature. Moreover, the values listed

(Perrin 1982) from three other researchers agreed with the value at 25°C reported by

Morris. Therefore Equation 2-9, giving the potential to estimate temperature effect, is

used in this work.

Re-evaluation of k1 i

The five papers in Table 2-2 were reviewed in the order listed. The experimental

conditions used by these studies are summarized in Table 2-3. The updated KaHOCl and

KaNH4 were used during the recalculation of k1.

i Due to the limited raw data reported in the literatures, the values of k1 were recalculated

using the reported kobs values.

13

Weil and Morris (1949) conducted experiments at (Cl2/N)0 from 0.2 to 0.5 and ionic

strength from 0.001 to 0.21. The reactions were monitored through colorimetrically

measuring the decrease of unreacted free chlorine (HOCl and OCl-). And some were

checked spectrophotometrically following the increase of monochloramine at 245nm.

Samples were taken at about every minute in a 5 minute period. Limited by the

experimental technique at the time and the fast reaction rate between pH 6.5 and 10, the

experiments were only conducted at pH less than 6.5 and above 10.5, using concentration

in the order of 10-5 M.

Table 2-3 Experimental Conditions for Monochloramine Formation Reaction

Sources Temp, °C pH Ionic strength

μ, M (Cl2/N)0 k1 at 25°C,

M-1s-1 Duration

Weil & Morris 1949 5.9 - 35 4.5 - 6.5,

10.5 - 12.5 0.0001 - 0.21 0.2 - 0.5 6.20E+06 5 min Margerum et al 1978 25 5.5 - 10 0.1 0.02 2.80E+06 N/A

Johnson & Inman 1978 25 7.4-11 0.003, 0.031-0.406 0.067 3.10E+06 90 ms Morris & Isaac 1983 3.9 - 34.1 6.95 0.009 - 0.091 0.1, 0.25 4.20E+06 350 ms Qiang & Adam 2004 5 - 35 6-12 0.075 0.05 - 0.1 3.07E+06 20 -5000 ms

Weil and Morris used the integration approach to obtain the value of k1. The second

order reaction, illustrated by Equation 2-10, is integrated into Equation 2-12.

NTClTobs CCkdt

ClNHd,,

2 ][⋅= Equation 2-10

CT,Cl – total free chlorine concentration, M CT, N – Total free ammonia concentration, M

⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+

⋅=

−−

−−

+−

+

aHOClpH

pH

aNHpH

aNHobs KK

Kkk

γγ

γγ

1010

101

4

4 Equation 2-11 (from Equation 2-7)

k1 – specific rate coefficient, M-1s-1 Ka – acid dissociation constant for corresponding species, M γ - activity coefficient of the corresponding species

14

ClTNT

NTClT

ClTNTobs CC

CCCC

tk,0,

,0,

0,0,

ln)(

1⋅

⋅

−=⋅ Equation 2-12

Given that monochloramine formation is the only undergoing reaction, the rate of

monochloramine increase is equal to the rate of decrease in total free chlorine CT,Cl or that

of total free ammonia CT, N. kobs can be obtained as the slope of plotting the right hand

side of Equation 2-12 against time t. The specific rate coefficient k1 can then be

calculated using Equation 2-11 (see derivation in Ionic Strength Correction section).

The recalculated k1 values showed variation over pH, e.g. the values obtained from

experiments conducted under pH 6.5 (5.33x106 -7.63x106 M-1s-1) are consistently higher

than those from pH higher than 10 (3.94x106 – 5.40x106 M-1s-1). This may be due to the

interferences at lower pH from the side reactions, such as dichloramine formation, which

would cause a faster decrease of free chlorine. In another study by Leao (Leao 1981),

significant dichloramine production was found after one minute at pH 6.64 and (Cl2/N)0

0.05 to 0.5. Although the concentration Leao used was two orders of magnitude higher

than what Weil used, this suggests that dichloramine formation could be the potential

interference under pH 6 – 7 and (Cl2/N)0 less than 0.5. Thus the values obtained at pH

less than 6.5 are excluded from this re-evaluation process.

The second study listed in Table 2-2 was conducted by Huffman and Margerum

(Huffman 1976; Gray, Margerum et al. 1979). They used stopped-flow

spectrophotometer and measured the formation of monochloramine at 243nm. The molar

ratio (Cl2/N)0 was 0.02 and ionic strength was 0.1. The concentration of the reactants was

on the order of 10-5 M.

15

Due to the low (Cl2/N)0 used, the reaction was assumed to be pseudo-first order, with

constant ammonia concentration. The kobs was obtained by plotting monochloramine

formation rate vs. the concentration of total free chlorine, as shown in Equation 2-13.

ClTobsCkdt

ClNHd,

2 ][= Equation 2-13

NTaHOCl

pH

pH

aNHpH

aNHobs C

KKK

kk ,4

4

1010

101 ⎟⎟

⎠

⎞⎜⎜⎝

⎛+⋅⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+

⋅=

−−

−−

+−

+

γγ

γγ

Equation 2-14

The specific rate coefficient k1 can be calculated using Equation 2-14.

The kobs values were reported throughout a range of pH, 5.5 – 9.5 (Huffman 1976), from

which the recalculated values of k1 were higher at pH less than 6.98. One potential cause

could be that HOCl, which has the maximum absorbance at 235nm, may interfere with

NH2Cl detection at 243nm, when pH is less than pKaHOCl.

To evaluate this hypothesis, a model was developed for monochloramine formation

reaction only. The reported experimental conditions were used as input to simulate

concentrations over time for NH2Cl and HOCl. Subsequently the absorbance of the two

species were calculated by using the reported molar absorptivity, 445 M-1cm-1 for NH2Cl

at 243nm (Qiang and Adams 2004) and 96.5 M-1cm-1 for HOCl at 240nm (Morris 1966).

The degree of interference was represented by the ratio of absorbance of HOCl and

NH2Cl (AbsHOCl240/AbsNH2Cl243). At the initial stage of data collection, a ratio larger than

20% infers a significant interference from HOCl, while a ratio less than 20% indicates the

opposite.

The average of all the recalculated k1 values from Huffman and Margerum, 2.86x106 M-

1s-1, was used for simulation. The duration of the experiment was not reported (Huffman

16

1976; Margerum, Gray et al. 1978). Nevertheless according to the 90 to 350 milliseconds

used by other researchers, 50ms was assumed as the initial stage of the data collection

and at which the potential interference from HOCl was evaluated. The results showed

that at pH 5.65, AbsHOCl240/AbsNH2Cl243 is 1074%. Therefore a large interference at 243nm

from HOCl is expected. At pH 6.89, this percentage decreased to 55%, and at pH 7.28, it

dropped to 20%.

Using the model-generated concentrations of NH2Cl, kobs and k1 were back calculated

through Equation 2-13 and 2-14. When the interference of HOCl was considered, in other

words, the absorbance of HOCl was included in the total absorbance for NH2Cl, the

straight line obtained from Equation 2-13 moved towards the origin. Yet the slope (kobs)

did not show any significant difference, compared to that when no interference was

included. This led to the conclusion that although the interference from HOCl on NH2Cl

was significant at certain time point, it did not affect the values of kobs or k1.

Another possible cause of the variation of k1 over pH is the values chosen for the

dissociation constants. Yet as stated before, these constants were carefully reviewed and

believed to be the most reliable.

The third study listed in Table 2-2 was conducted by Johnson and Inman (1978) at 25°C,

ionic strength from 0.003 to 0.406, pH from 7.4 to 11, and (Cl2/N)0 at 0.067. Stopped-

flow spectrophotometry was used to monitor monochloramine increase over a time

period of 90 milliseconds. Pseudo-first order reaction was assumed. Therefore kobs and

k1were calculated using Equation 2-13 and 2-14 respectively. The same exploration was

carried out as for Huffman’s study. The result showed that the interference of HOCl at

243 nm had no significant impact on k1.

17

In the fourth study in Table 2-2, Morris and Isaac (1983) used k1 values reported in their

earlier publication (Morris and Isaac 1980). Stopped-flow technique was used to conduct

experiments under the following conditions, temperature 3 to 35°C, pH 6.95, and ionic

strength 0.009 and 0.091. Two molar ratios, (Cl2/N)0, were used, 0.1 and 0.25. Equation

2-11 was used to recalculate k1 using the reported kobs values.

In the last study listed in Table 2-2, Qiang and Adams (2004) used stopped-flow

spectrophotometry over a pH range of 6-12 and a temperature range of 5 to 35°C.

Monochloramine formation was monitored with five replicates conducted for each

experiment. The calculation and acid dissociation constants used in their study are

consistent with this work. Thus the reported values are used directly without

recalculation.

Other than those k1 values obtained at pH lower than 6.5 reported by Weil and Morris, all

other recalculated k1 from the listed references in Table 2-3 are compiled into one table

(see Appendix A) and used in the following correlation analysis. In each study, when pH

is the only difference among all experimental conditions, the variation of k1 over pH

never exceeded 0.8x106 M-1s-1. Therefore this variation was considered as the inherent

randomness and k1 values are averaged.

Correlation analysis

In order to answer the first of the two questions, k1 values are grouped by (Cl2/N)0 and

plotted against ionic strength, as shown in Figure 2-1. No consistent trend can be

observed at all (Cl2/N)0. This suggests that among all the available data in the literature,

k1 does not show any significant correlation with ionic strength.

18

0.E+00

1.E+06

2.E+06

3.E+06

4.E+06

5.E+06

6.E+06

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45u, M

k1, M

-1s-

1

(Cl2/N)0=0.5

(Cl2/N)0=0.06

(Cl2/N)0=0.05

Figure 2-1 Correlation of k1 and ionic strength at different initial (Cl2/N)0 , T=25°C

Correlation of k1 with (Cl2/N)0 at different ionic strength is plotted in Figure 2-2. The

data points at (Cl2/N)0 0.2 and beyond are all from Weil and Morris’s study and present a

rather flat trend. Meanwhile those from the other four investigators are all less than 0.1 in

(Cl2/N)0 and quite scattered. Although overall there seems to be a trend, it is not as

convincing as if data from a single study covers the entire range of (Cl2/N)0. One thing

worth mentioning in Huffman and Margerum’s study was that Huffman (1976)

conducted a few experiments to explore the possible effect of (Cl2/N)0 on k1. He

concluded that when (Cl2/N)0 was between 0.02 to 0.05, it did not affect k1. Again this

does not offer any information beyond (Cl2/N)0 0.1. If k1 was found to be correlated with

(Cl2/N)0, the second order mechanism for monochloramine formation would not hold.

The inconclusive trend observed in Figure 2-2 cannot challenge this mechanism proposed

by Morris. Nevertheless it suggests that at high (Cl2/N)0, e.g. between 0.2 to 1, the

reaction might follow a different mechanism. Further study using stopped-flow

19

spectrophotometry is needed to investigate monochloramine formation reaction at

(Cl2/N)0 between 0.2 and 1.

0.E+00

1.E+06

2.E+06

3.E+06

4.E+06

5.E+06

6.E+06

0 0.1 0.2 0.3 0.4 0.5 0.6 (Cl2/N)0

k1, M

-1s-

1

u=0.01 u=0.03u=0.05 u=0.075u=0.1 u=0.21

Figure 2-2 Correlation of k1 and (Cl2/N)0 at different ionic strength, T=25°C

Figure 2-3 shows the best fitted lines to the data from three of the investigators who

studied k1 at different temperatures. The Arrhenius Equation from Weil and Morris

shows a significantly higher sensitivity (larger frequency factor and higher activation

energy) to temperature than those from the other two investigators. This could be another

evidence of an alternative mechanism when (Cl2/N)0 is between 0.2 and 1.

There is no raw data available from the literature to explore the possibility of an

alternative mechanism. Nor is it the purpose of this work to conduct detailed kinetic

experiments. Thus the second order mechanism is believed to hold and the data from

Appendix A are used in the formulation of the Arrhenius Equation.

As presented in Figure 2-4, the new Arrhenius Equation is k1=2.04x109exp(-1887/T),

which gives 3.63x106 M-1s-1 at 25°C.

20

In the Unified Model, the value from the critical review of Morris and Isaac (1983) was

used, with Arrhenius Equation 6.6x108exp(-1510/T) and a value of 4.20 x106 M-1s-1 at

25°C. The re-calculated Arrhenius Equation has larger activation energy as well as larger

frequency factor, which in combination results in a smaller value at 25°C.

Figure 2-3 k1 as a function of temperature from different sources

Figure 2-4 Specific rate constant of k1 as a function of temperature

21

2.2.2 Rate coefficient for other reactions

The other reactions in the reaction scheme were not as extensively studied as

monochloramine formation reaction. In addition, there is no new literature available since

the development of the Unified Model. Thus a brief review was carried out to introduce

the rate coefficient for each reaction.

The equilibrium constants mentioned in this section are solely for showing the derivation

of some of the rate coefficients. They are not used in the model calculation because at

low concentration (10-5 M in drinking water treatment), the reactions are kinetic-

controlled and will hardly ever reach equilibrium in the duration that is concerned in

drinking water treatment.

Reactions and rate coefficients in the combined region

Reaction 2 is the reverse reaction of Reaction 1, the hydrolysis of monochloramine.

Granstrom (Granstrom 1954) proposed that the hydrolysis of monochloramine was the

first order part of the disproportionation of monochloramine, which also comprised of a

second order part. The rate coefficient for this reaction was studied under ionic strength

of 0.45M, pH less than 5.2, and temperature 5 to 50°C. Morris and Isaac (1983)

reevaluated Granstrom’s data and derived k2 = 1.38x108exp(-8800/T) s-1, with a value of

2.1x10-5 s-1 at 25°C. Using k1 and the equilibrium constant measured (see next paragraph)

at 25°C and 0.5M ionic strength, Margerum (1978) calculated k2 to be 1.9x10-5 s-1, which

is in good agreement (less than 10% difference) with that reported by Morris and Isaac.

The hydrolysis constant K1 of monochloramine can be calculated as k2/k1. Using k1

from this work and the k2 formula reported by Morris and Isaac (1983), K1 is calculated

22

to be 6.90x10-2exp(-6913/T) M, with a value of 5.81x10-12 M at 25°C. This value is in

between the value reported by Gray et al. (Gray, Margerum et al. 1979), 6.7x10-12 M at

ionic strength 0.5 M, and the value calculated from the formula proposed by Morris and

Isaac (1983), which is 5.0x10-12 M.

Reaction 3 is the major pathway of dichloramine formation when free chlorine is present.

This reaction was first studied by Morris et al (Morris, Weil et al. 1950) and then Palin

(Palin 1950) by determining the distribution of monochloramine and dichloramine and

evaluating k3 relative to k1. Later studies by Wei (1972) and Saunier (1976) investigated

this k3 under breakpoint chlorination process. Mangerum et al (Margerum, Gray et al.

1978) used stopped-flow spectrophotometer to monitor this reaction directly at 0.5 and

0.1 ionic strength and 25°C. After reevaluation of the above reported data, Morris and

Isaac achieved a compromise line with the expression of k3=3.0x105exp(-2010/T) M-1S-1

and a value of 3.5x102 M-1S-1 at 25°C.

Reaction 4 is the hydrolysis of dichloramine. Morris and Isaac (1983) obtained a value of

7.6x10-7 s-1 through thermodynamic operations of K1, K5, and k3 (k4=k3xK1/K5).

Margerum et al (1978, 1979) calculated the value of k4 to be 6.5x10-7 s-1 at 25°C and

0.5M ionic strength using experimentally obtained k3 and K3 (the hydrolysis equilibrium

constant of dichloramine, K3=k4/k3). This value is more favorable than that reported by

Morris and Isaac due to its experimental basis instead of calculation based on equilibrium

constants of Reaction 1 and 5.

Reaction 5 is believed to be the major dichloramine formation pathway when excess

ammonia is more than 1mg/L (Valentine, Ozekin et al. 1998). It was first studied by

Granstrom (1954) as part of the disproportionation of monochloramine which was found

23

to proceed partly through Reaction 5 and partly through monochloramine hydrolysis

(Reaction2). The proposed rate equation was d[NHCl2]/dt=k1[NH2Cl]+k2[NH2Cl]2 as in

Granstrom’s dissertation (1954), where the first order term represents monochloramine

hydrolysis and the second order term was hypothesized to be acid catalyzed. The

experimental conditions used were pH 4.2 to 5.2 with acetate buffer, and ionic strength

0.15 to 0.45 M. The rate coefficient for the second order reaction given by Granstrom

(1954) was k2= (4.75x103+6.3x108[H+] +1.68x105[CH3COOH])exp(-4310/RT) M-1min-1.

Jafvert (1985) further investigated the second order, general acid catalyzed reaction at

25°C using phosphorus buffer (pH 3-4) at ionic strength of 0.2M. Under such

experimental conditions, monochloramine hydrolysis was too slow to compete with the

second order reaction (Jafvert 1985). Thus Reaction 5 can be isolated and studied alone.

The catalytic rate coefficients H+, H3PO4, and H2PO4- were determined to be

kH+=6.35x103 M-2s-1, kH3PO4= 870 M-2s-1, kH2PO4-=11 M-2s-1. The catalytic rate coefficient

of sulfate buffer was also determined. These k values were plotted against the

corresponding Ka values and the linear free energy diagram showed a good correlation

(Jafvert 1985). Nevertheless, these catalytic rate coefficients were obtained from the

intercepts of the plots from limited data, which made them susceptible to large variability.

Jafvert (1985) especially pointed out that the value for kH2PO4- was considered only as a

rough estimation. The rate expression adopted in the Unified Model was

k5=8.33x103[H+]+888[H3PO4]+0.36[H2PO4-] M-1s-1. Apparently some adjustments were

made during calibration.

The catalytic effect from carbonate is difficult to evaluate experimentally due to the

interference from atmospheric carbon dioxide at low pH (Valentine and Jafvert 1988).

24

However it can be estimated using the linear free energy relationship, more specifically

the Brönsted Equation. The catalytic power and acid-base strength was found to correlate

with each other as shown in Equation 2-15 (Bell 1978).

21 )]log([)log( CQPpKC

Pk

ai ++= Equation 2-15

C1,C2 - constants ki - the catalysis rate coefficient Ka - the acid dissociation constant P - the number of exchangeable protons on the acid Q - the number of protons that the conjugate base could accept

For those catalytic species with known catalytic rate coefficients, the value of log(ki/P)

was plotted against pKa+log(P/Q). As shown in Figure 2-5, a linear relationship was

achieved from which the catalysis rate coefficients for carbonate and silicate were

estimated from their acid dissociation constants. The estimated values for carbonate

species were kH2CO3= 0.75 M-2S-1, and kHCO3-= 2.0x10-3 M-2S-1, which are expected to

have much less significance on monochloramine disproportionation when compared to

hydrogen ion (kH+=6.35x103 x103 M-2S-1).

25

Figure 2-5 Linear Free Energy Relationship (Bronsted Plot)

Relating species-specific catalysis rate constants to acid dissociation constants.

Solid squares, measured values; hollow squares, predicted. 95% confidence region shown. (Valentine et al, 1988)

In 1998, Valentine et al (Valentine, Ozekin et al. 1998) studied monochloramine decay in

carbonate buffer system using a model which only consisted of Reaction 1 to 10 from the

Unified Model. The catalytic coefficients for carbonate species reported earlier

(Valentine and Jafvert 1988) were found not sensitive enough to the changes in carbonate

buffer concentrations. To correct this, a computer program was developed to estimate the

coefficients by fitting the experimental data (Valentine, Ozekin et al. 1998). The updated

values at 25°C are kH2CO3= 4x104 M-2hr-1 (11.11 M-2s-1), and kHCO3-=800 M-2hr-1 (0.22 M-

2s-1). These are respectively one and two orders of magnitude larger than those reported

in 1988 (Valentine and Jafvert 1988). The values of kHCO3- and kH2CO3 at different

temperatures were also obtained through data fitting and the Arrhenius Equations were

formulated for the two rate coefficients. Regarding kH+, Valentine et al (1998) adopted

26

the Arrhenius Equation developed by Granstrom (1955), which at 25°C has a value of

7.25x103 M-2s-1 and is fairly comparable to 6.35x103 M-2s-1 (Jafvert 1985; Valentine and

Jafvert 1988). These updates on the catalytic rate coefficients abandoned the linear free

energy relationship and indicated that Reaction 5 is the only other important reaction,

besides the first three reactions, of which the rate coefficients were a function of

temperature. Since the linear free energy relationship is an empirical method itself and

could lead to order of magnitude difference in coefficient values through its estimation in

log scale, the later values from Valentine (1998) are adopted in this study as shown in

Table 2-4.

Reaction 6 is the reverse of Reaction 5, which theoretically should also be an acid

catalysis reaction. Yet due to the difficulty in direct measurement, this reaction was never

studied alone. When studying dichloramine decomposition in the presence of ammonia,

Hand and Margerum (1983) proposed the following reaction scheme:

++

++

+↔+

⎯⎯ →←+

HClNHClNHNH

ClNHHNHClNHClHK

2223

222

2

2

The rate expressions in terms of monochloramine and dichloramine formation are,

+

+

+

+

⋅=

=−

=

4

4

4

2342

2442

26

]][][[2/1][

]][[][

NH

NH

NH

NH

NH

Kk

k

KNHClHNHk

dtNHCld

NHClNHkdt

ClNHd

Hand and Margerum (1983) reported the value of kNH4 to be 3x10-5 M-1s-1 at 25°C and

0.5M ionic strength. KNH4+ at 25°C is 5.61x10-10 (pKa=9.25). Thus the rate coefficient for

Reaction 6 is calculated to be 2.67x104 M-2s-1 (Jafvert 2006).

27

Dichloramine decomposition was found to be significant for oxidant loss in both

combined and break point regions. Reactions 7 to 9 were first proposed by Wei (1972) in

his study of breakpoint chlorination. The intermediate was hypothesized and formulated

as NOH, of which the formulation would have no effect on the model simulation (Wei

1972). Reaction 7 was found to be specific base catalyzed. The rate coefficient values at

25°C proposed by Wei are k7= 1.12x105 M-1s-1, k8= 2.46x103 M-1s-1, and k9= 2.50x104

M-1s-1. Leao (1981) included these reactions when studing combined chlorine kinetics

and found that dichloramine decomposition in the absence of free chlorine was first order

in dichloramine and inversely proportional to hydrogen ion concentration. After

reorganizing k7 to the same format as in Table 2-4, the rate coefficients used by Leao

were 112.5 M-1s-1 for k7, 2.78x104 M-1s-1 for k8, and 8.33 x103 M-1s-1 for k9. The values

of these coefficients were mostly obtained from data fitting and keeping the intermediate

at low concentration at all times (Leao 1981). When these reactions were used to account

for dichloramine loss in breakpoint region, the value of k7 was three orders of magnitude

higher than when they were only used for combined region dichloramine loss.

Jafvert (1985) adopted this reaction scheme and re-evaluated the coefficients for these

reactions in the presence of excess ammonia. Dichloramine solution, formed by dropping

the pH of a monochloramine solution between 3.9 and 4.0, was mixed with buffer

solution (a mixture of ammonia and phosphate buffer) at pH 8 to 10. This mixture

contained different concentrations of monochloramine. The change in concentrations of

monochloramine and dichloramine over time was monitored. Reaction 6, which can be a

side reaction was believed to be very slow in this pH range and did not interfere with the

reactions studied (Jafvert 1985). The HOCl produced through Reaction 8 would react

28

with the excess ammonia to form monochloramine. Thus Reaction 1 was included in the

code described below. Due to the large value of k1, it would not be the rate limiting

reaction (Jafvert 1985).

A computer code (Jafvert 1985) was set up in FORTRAN to estimate the three rate

coefficients by fitting a set of experimental data. Since it was assumed that the

intermediate was always at a very low concentration and pseudo-steady state, both k8 and

k9 had to be very large. Jafvert (1985) assigned a ratio between k8 and k9 to minimize

the time needed for the code to converge. This ratio also determines the net stoichiometry

of monochloramine formation and dichloramine decomposition. These reactions were

also found to be non-catalytic by general acid or base, which is different from the

decomposition of dichloramine when free chlorine is present.

The averaged values were reported to be k7=1.62x102 M-1s-1, k8=2.78x104 M-1s-1 and

k8/k9=3.3. The value of k7 is consistent with that reported by Hand and Margerum

(1983), which was 150 M-1s-1. Although the ratio k8/k9 was found to be a function of pH,

it did not appear to be significant (Jafvert 1985). This could be the result of the inclusion

of monochloramine formation reaction which is pH dependent (see section on k1). The

final values for k8 and k9 adopted by Jafvert (1985) were 1.66x106 M-1min-1 (2.77x104

M-1s-1), and 5.0x105 M-1min-1 (8.3x103 M-1s-1) respectively.

In his later paper (Jafvert and Valentine 1987), a slightly different value for k7 was

reported (1.62x102 M-1s-1) and the values for k8 and k9 were five orders of magnitude

larger than those reported in 1985, which reveal the empirical nature of these proposed

reactions. Nevertheless this is the only study where these reactions were isolated from

other possible reactions. Although reaction schemes using other possible intermediates

29

were suggested by different investigators (Saunier 1976; Diyamandoglu 1989), all need

to be proved experimentally. Until then, the reaction scheme used by Jafvert is adopted as

it was proved to work in the Unified Model.

Reaction 10 was first proposed by Leao (1981) in his combined chlorine model in order

to have the model output better correspond with the experimental data. Jafvert adopted

this reaction in the Unified Model and obtained k10=55 M-1hr-1 (1.5x10-2 M-1s-1) through

calibration. The chlorine concentration used in Leao’s work was from 50 to 100 mg/L as

Cl2. The Unified Model was calibrated to chlorine concentration range from 10 to 50

mg/L as Cl2. These concentrations are beyond the Maximum Residual Disinfectant Level

(MRDL) requirement of 4 mg/L as Cl2 (EPA July, 2008).

Reactions in breakpoint region

Reaction 11 is trichloramine formation reaction, or the decomposition reaction of

dichloramine in the presence of free chlorine. Hand and Margerum (1983) studied this

reaction using stopped-flow techniques and found that with the absence of free ammonia,

dichloramine is autocatalytic and sped up as NCl3 and HOCl (through Reaction 12) are

formed. The reaction of NHCl2 and HOCl is general base catalyzed and produces NCl3,

which in turn reacts with NHCl2 in another base-catalyzed reaction (Reaction 12) to give

N2, Cl-, and HOCl. When free chlorine concentration is very high, Reaction 11 is

predominant. Experiments were conducted at 0.5 M ionic strength and various pH values

(6 – 12), using ammonia free dichloramine (Hand and Margerum 1983). Through

simultaneous multiple linear regression, Hand and Margerum reported the base catalytic

rate coefficients to be kOH=3.3x109 M-2s-1, kOCl-=1x105 M-2s-1, and kCO32-=6x106 M-2s-1 at

25°C. These values were found to fit the linear free energy relationship fairly well.

30

As stated in the previous paragraph, Reaction 12 is one of the reactions that happen to

dichloramine when free chlorine is present. Trichloramine generated through Reaction 11

will react with dichloramine, especially when free chlorine concentration is less than

dichloramine. This reaction is a base catalyzed reaction (Hand and Margerum 1983;

Kumar, Shinness et al. 1987; Yiin and Margerum 1990) and is very rapid in neutral or

basic solutions. Yiin and Margerum (1990) evaluated this reaction at pH 6.13-6.88 and

ionic strength 0.5M and reported the catalytic rate coefficient for HPO42- to be 2.92x104

M-2s-1. No other catalytic rate coefficients were reported due to the instability of the

reactant at higher pH. Nevertheless, Yiin and Margerum suggested that the catalytic rate

coefficient for OH- would be greater than 4x107 M-2s-1. In the Unified Model, Jafvert and

Valentine (1992) assumed that only OH- catalysis was taken into account in the reaction

and the rate coefficient was determined empirically through data fitting. This approach is

adopted in this study, since the catalytic rate coefficients of carbonate system are not

available and the limited reported coefficients preclude the estimation using free linear

energy relationship.

Reaction 13 and 14 were postulated by Jafvert (Jafvert 1985; Jafvert and Valentine 1992)

as part of the reaction scheme in breakpoint region. Reaction 13 is similar to Reaction 12

and was assumed to have a pH dependency with an empirical rate coefficient. Reaction

14 is the only reaction which accounts for the formation of nitrate. It was assumed to

follow the same reaction steps as N2 formation (Wei 1972; Saunier 1976). Jafvert (1985,

1990) formulated the rate expression based on the pH dependency reported by Pressley et

al (Pressley, Dolloff et al. 1972). To date, no experimentally proved reaction mechanism

31

was reported in the literature for nitrate formation during breakpoint reactions. The rate

coefficient of Reaction 14 was obtained empirically (Jafvert 1985).

Equilibrium reactions

In the Unified Model, equilibrium of hypochloric acid, ammonium, and carbonic acid

was assumed to prevail under all conditions. The equilibrium reactions of these species

were also included in the model (Jafvert 1985).

2.3 Trichloramine hydrolysis reaction

Trichloramine is an important species of the breakpoint reactions. Its hydrolysis pathway

as shown below was not included in the Unified Model.

NCl3 + H2O → NHCl2 + HOCl

This reaction was first studied by Saguinsin and Morris (1975). Saunier included this

reaction in the reaction scheme of a breakpoint model (Saunier 1976). However the rate

coefficient used for this reaction was empirical (Saunier 1976). Kumar and Margerum et

al. (1987) studied this reaction together with Reaction 12 under pseudo-first order

condition with excess hydroxide or buffer. They reported the rate expression as follows,

]])[NCl[HB][OHk+][OHk+][OHk+(k2][

3-

HB2-

2-

103 =−

dtNCld

The factor 2 is the result of the overall stoichiometry of base decomposition of NCl3

(NCl3 hydrolysis and Reaction 12).

2NCl3 + 6OH- → N2 +3OCl- +3Cl- + 3H2O

32

As shown in the rate expression, this reaction is a specific base/general acid catalyzed.

The reported rate coefficients relevant to this study are k0=1.60x10-6 s-1, k1=8 M-1s-1,

k2=890 M-2s-1, kHCO3-=65 M-2s-1, at 0.5 M ionic strength. As stated before, Reaction 12 is

very rapid. Thus trichloramine hydrolysis is the rate control reaction, for which the rate is

half of that for the two reactions combined. This reaction will be included in the reaction

scheme of this study and referred as Reaction 15.

A summary of all reactions and the corresponding rate coefficients are listed in Table 2-4.

There are a total of 15 reactions and 22 rate coefficients, within which only 21 are

independent. The value of k9 is dependent on k8 at a ratio of 3.2 to ensure the balance

between monochloramine and dichloramine in the combined region (Jafvert 1985).

33

Table 2-4 Reaction Scheme and Rate Coefficients for the Unified Plus Model

No. Reactions Rate expression Rate coefficients Reference for rate coefficients

1 HOCl + NH3 → NH2Cl + H2O k1[HOCl][NH3] k1=2.04x109xexp(-1887/T) M-1s-1 This work 2 NH2Cl + H2O → HOCl + NH3 k2[NH2Cl] k2 = 1.38x108exp(-8800/T) s-1 Morris and Isaac,1983 3 HOCl + NH2Cl → NHCl2 + H2O k3[HOCl][NH2Cl] k3=3.0x105exp(-2010/T) M-1s-1 Morris and Isaac, 1983 4 NHCl2 + H2O → HOCl + NH2Cl k4[NHCl2] k4=6.5x10-7 M-1s-1 Margerum 1978 5 NH2Cl + NH2Cl → NHCl2 + NH3 k5[NH2Cl][NH2Cl] k5 = k5H[H+] + k5HCO3-[HCO3-] + k5H2CO3[H2CO3] Jafvert 1985 k5H=3.78x1010exp(-2169/T)/3600 M-2s-1 Granstrom,1954 k5HCO3-=1.5x1035exp(-22144/T)/3600 M-2s-1 Valentine 1998, empirical k5H2CO3=2.95x1010exp(-4026/T)/3600 M-2s-1 Valentine 1998, empirical

6 NHCl2 + NH3 → NH2Cl + NH2Cl k6[NHCl2][NH3][H+] k6=2.67x104 M-2s-1 Jafvert, 2006 7 NHCl2 + H2O → NOHa + 2HClb k7[NHCl2][OH-] k7=1.67x102 M-1s-1 Jafvert 1985 8 NOHa + NHCl2 → HOCl + N2

b + HCl b k8[I][NHCl2] k8=2.77x104 M-1s-1 Jafvert 1985 9 NOHa + NH2Cl → N2

b + HCl b + H2Ob k9[I][NH2Cl] k9=8.3x103 M-1s-1 Jafvert 1985 10 NH2Cl + NHCl2 → N2

b + 3HClb k10[NH2Cl][NHCl2] k10=1.53x10-2 M-1s-1 Jafvert 1985, Empirical 11 HOCl + NHCl2 → NCl3 + H2O k11[HOCl][NHCl2] k11 = k11OH-[OH-] + k11OCl-[OCl-] + k11CO3--[CO3--] Hand and Margerum, 1983

k11OH-=3.28x109 M-2s-1 Hand and Margerum, 1983 k11OCl-=9.00x104 M-2s-1 Hand and Margerum, 1983 k11CO3--=6.00x106 M-2s-1 Hand and Margerum, 1983

12 NHCl2 + NCl3 + 2H2O → 2HOCl + N2b + 3HClb k12[NHCl2][NCl3][OH-] k12=5.56x1010 M-2s-1 Jafvert 1985, Empirical

13 NH2Cl + NCl3 + H2O → HOCl + N2b + 3HClb k13[NH2Cl][NCl3][OH-] k13=1.39x109 M-2s-1 Jafvert 1985, Empirical

14 NHCl2 + 2HOCl + H2O → NO3- + 5H+ + 4Cl- k14[NHCl2][OCl-] k14=2.31x102 M-1s-1 Jafvert 1985, Empirical

15 NCl3 + H2O → NHCl2 + HOCl k15[NCl3] k15=k150+k151[OH-]+k152[OH-]2+k15HCO3-[HCO3-][OH-] Kumar et al, 1987 k150=1.60x10-6 s-1 Kumar et al, 1987 k151=8 M-1s-1 Kumar et al, 1987 k152=890 M-2s-1 Kumar et al, 1987 k15HCO3-=65 M-2s-1 Kumar et al, 1987

a Assumed formula for the unidentified intermediate. b Products and stoichiometry are assumed for balancing the reaction. Possible products may include N2, H2O, Cl-, H+, NO3


34

3 Model Setup

The 15 reactions listed in Table 2-4 are used as the reaction scheme to develop the

Unified Plus Model. The equilibrium reactions of HOCl, NH4+, and H2CO3 are also

included. The effect of ionic strength on these equilibrium reactions is modeled using the

Güntelberg approximation of the DeBye-Hückel law (Snoeyink and Jenkins 1980) .

2/1

2/1

15.0

logμ

μγ

+=− −+ZZ

Equation 3-1

Z – the charge number of the ion μ - the ionic strength of the solution γ - the activity coefficient

The change of pH is modeled using buffer intensity as shown in Equation 3-2

βAdC

dpH−

= Equation 3-2

CA – mole/liter of strong acid or H+ added β – buffer intensity

There are six state variables. They are monochloramine, dichloramine, trichloramine, free

chlorine, free ammonia, and pH. The value of pH can also be set to remain constant. The

inputs of the model include temperature, pH, ionic strength, total buffer concentration,

and the initial concentration of NH2Cl, NHCl2, NCl3, free chlorine, and free ammonia.

The model outputs are concentrations over time of all the species involved in this system

of reactions.

35

3.1 Model implementation using Visual Basic for Application

(VBA)

In order to develop the model into an easy-to-use tool, a straightforward user interface is

essential. Excel is chosen for this purpose due to its prevalent use while the model will be

developed in VBA to take advantage of the convenient interaction between code and the

user interface.

The user interface consists of multiple worksheets, which are “Input”, “Output”, and

charts of the concentrations over time for the species of interest. In the “Input”

worksheet, the user can specify the values for the input parameters as well as define the

run control parameters, such as computing time step, computing ending time, and

reporting time step. The “Output” worksheet hosts the tabular form of the simulated

concentrations at each reporting time step. From the simulated results in this worksheet,

the charts are generated to give the user a straightforward illustration of the model output.

The model is implemented through four VBA subs. They are “Main”, “Mass Balance”,

“Differential Equation”, and “Solver”. In the “Main” sub, the inputs are read in from

“Input” worksheet at the beginning of each simulation. And the values of all the reaction

coefficients are assigned. Then the “Mass Balance” sub is called at every time step to

calculate the speciation under equilibrium for carbonate species (H2CO3, HCO3-, and

CO32-), hypochlorous acid (HClO, ClO-), and ammonium (NH3, NH4

+). Subsequently

“Differential Equation” and “Solver” subs are called to solve the concentrations of all

species at the next time step. Lastly the outputs are printed to “Output” worksheet at each

reporting time step. In “Differential Equation” sub, differential equations for

36

monochloramine, pH, dichloramine, trichloramine, free chlorine, chloride, nitrogen gas,

and nitrate are defined. The “Solver” sub solves the set of differential equations using a

numerical method. The explicit method or Euler’s method is used due to its simplicity in

programming. An example of the solution for a simple first order reaction is illustrated in

Equation 3-3. In an age where the computing power is greatly enhanced, a very small

time step can be used to achieve stability as well as accuracy of the simulation result.

tckcc ttt Δ⋅⋅+=+1 Equation 3-3

Each differential equation was isolated and tested to avoid any error during

programming. Then mass conservation was checked throughout the simulation for

chlorine and nitrogen species. Necessary time steps were tested for the model to achieve

stability and accurate results under both combined and breakpoint reaction conditions. A

hundredth of a second was found to be the optimum computing time step. The source

code is included in Appendix E.

3.2 Sensitivity analysis

Sensitivity analysis was carried out to obtain a good understanding of the model,

specifically the response of the model under different reaction initial conditions to the

variations in the values of different rate coefficients. To cover the ranges of pH, total

carbonate buffer, and (Cl2/N)0, sixteen sets of initial conditions were designed for this

analysis as listed in Table D-1 of Appendix D. The two pH levels used, 7 and 9.5, will be

referred to as low and high pH. The same terminology will be used for describing total

carbonate buffer concentration, low and high buffer concentration for 0.001 and 0.01 M.

37

In order to determine the sensitivity of interested species to each rate coefficient,

parameter perturbation method was used (Chapra 1997). Under each initial condition, all

rate coefficients were kept at base values (kb) as listed in Table 2-4 except one

coefficient which was perturbated by using a set of scaling factors (sf =k/kb). The scaling

factor was designed to cover the range of values present in the literature for each rate

coefficient. Corresponding to each scaling factor of the perturbation, the changes in the

concentration of the interested species at a certain time point were also recorded as a ratio

(the ratio of change, rc=C/Cb). Six hours was used for initial conditions at (Cl2/N)0 0.5

and 0.9, while 30 minutes was used for initial conditions at (Cl2/N)0 1.2 and 1.7. After

perturbation of all the rate coefficients at each initial condition, a ratio of change over

scaling factor plot can be generated for each species. As shown in Figure 3-1, this plot

depicts the sensitivity of monochloramine to different rate coefficients at one tested initial

condition. However this type of plot does not allow comparison of the sensitivity that the

species shows to all rate coefficients across different initial conditions.

38

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

0.001 0.1 0.5 1 2 10 1000 100000Scaling Factor

Rat

io o

f Cha

nge

in M

onoc

hlor

amin

e C

once

ntra

tion

k1k2k3k5Hk5H2CO3k5HCO3k10k11CO3k11OCLk11OHk12k13k14k150k151k152k15HCO3k4k6k7k8&k9

Figure 3-1 Sensitivity of monochloramine to all reaction coefficients at 6 hours 20°C, pH=7, μ=0.01, CTCO3=0.01, initial free chlorine =5.6x10-5M, (Cl2/N)0=0.5

In order to achieve this purpose, the Condition Number (CN) (Chapra 1997) approach

was used to quantitatively express the result of parameter perturbation. In this case, the

CN is defined as the ratio of, the difference of the ratio of changes in concentration at

maximum and minimum scaling factors, and the difference of the maximum and

minimum scaling factors.

b

bsfsf

bb

sfbsfbsfsf

ck

kkcc

kk

kk

cc

cc

sfsfrcrc

CN ⋅−

−=

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛

=−

−=

minmax

minmax

minmax

minmax

minmax

minmax Equation 3-2

CN – condition number

rc – ratio of change, C/Cb Cb – the simulated concentration of the species of interest when k = kb

sf – scaling factor, k/kb kb – the base value of a rate coefficient as listed in Table 2-4

39

As shown in Equation 3-2, it is equal to the difference in concentrations at maximum and

minimum scaling factor normalized by Cb divided by the change in coefficient value

normalized by kb. This represents the effect of change in one rate coefficient, on the

predicted concentration of the species at one initial condition. If the response is linear, a

positive value indicates that the increase of k would cause an increase in the

concentration of the species at the point of time. And a negative value means a decrease

in concentration when the value of k increases. Since this ratio is normalized by the base

value of each k, kb, and the corresponding concentration of the species, Cb, for one

species, the CN can be compared across all coefficients and all initial conditions. The

larger the absolute value of CN one coefficient has, the more sensitivity the species has

towards this coefficient. There are a few cases where the response was not linear.

However using this approach did not change the order of sensitive coefficients under a

specific initial condition.

Table D-2 to D-6 in Appendix D listed the calculated CN for monochloramine,

dichloramine, free chlorine, trichloramine, and pH under the 16 set of initial conditions.

In the tables, each row of scenarios has the same initial pH. Under each scenario, the rate

coefficients are sorted from the smallest CN to the largest CN. The two coefficients

having the largest absolute CN values are the rate coefficients which the specific species

is most sensitive to. The coefficient with the smallest absolute CN value is the least

sensitive. The results are discussed and summarized in the followings paragraphs.

Sensitivity of Monochloramine to various rate coefficients

40

In the combined region, i.e. (Cl2/N)0 at 0.5 and 0.9, at pH 7 monochloramine is most

sensitive to its formation reaction, and dichloramine formation reaction. Monochloramine

hydrolysis reaction is also very important. At pH 9.5, the above reactions as well as

monochloramine disproportionation reaction are more important relative to the other

reactions. However the sensitivity of monochloramine at high pH is far less than that at

pH 7 (The CN is one order of magnitude smaller at pH 9.5 than at pH 7).

At molar ratio 1.2 and pH 7, monochloramine is most sensitive to its formation and

dichloramine formation reaction. Trichloramine formation and monochloramine

hydrolysis reactions are also very important. At pH 9.5, monochloramine is most

sensitive to dichloramine formation reaction. Reaction 7, 12, and 13, i.e. dichloramine

decomposition pathways in the absence or presence of free chlorine are also important at

high pH.

At molar ratio 1.7 and pH 7, monochloramine is most sensitive to dichloramine formation

reaction, trichloramine formation reaction, and Reaction 14. Reaction 12 is also important

under this initial condition. At pH 9.5, dichloramine formation reaction is the most

important. Trichloramine formation, dichloramine decomposition (Reaction 7 and 12)

and Reaction 13 also show some importance. At different pH, the change of k12 would

have opposite effect on monochloramine loss. At pH 7, increasing k12 would expedite

monochloramine loss, while at pH 9, this would defer monochloramine loss.

Sensitivity of dichloramine to various rate coefficients

In the combined region, at pH 7, dichloramine is most sensitive to its formation and

decomposition reaction, as well as monochloramine formation and hydrolysis reaction.

Monochloramine disproportionation and trichloramine formation reactions are also

41

important at this pH. At pH 9.5, dichloramine is most sensitive to its decomposition and

formation reactions, monochloramine disproportionation, formation, and hydrolysis

reactions.

At molar ratio 1.2 and 1.7 (in transition and breakpoint regions) at both pH levels,

dichloramine is most sensitive to its formation and trichloramine formation reactions.

Dichloramine decomposition reaction is also an important reaction in both of these

regions. At (Cl2/N)0 1.2, high sensitivity is shown to monochloramine formation and

hydrolysis reactions at pH 7. At pH 7 and molar ratio 1.7, Reaction 12 and 14 are

important. While at high pH of both molar ratio 1.2 and 1.7, Reaction 12 and 13 were

important.

Sensitivity of free chlorine to various rate coefficients

In the combined region, free chlorine shows the highest sensitivity to monochloramine

formation and the reverse hydrolysis reactions. At pH 7, dichloramine formation reaction

is also important.

At molar ratio 1.2 and 1.7, free chlorine is most sensitive to dichloramine formation

reaction, although much smaller CN values are shown at pH 9.5 than at pH 7 (see Table

D-4). The other important reactions at pH 7 are monochloramine hydrolysis and

formation, trichloramine formation, dichloramine decomposition and hydrolysis reactions

at (Cl2/N)0 1.2, and trichloramine formation, Reaction 12 and 14 at (Cl2/N)0 1.7. At pH

9.5, other than dichloramine formation, free chlorine does not show significant sensitivity

toward any other reactions.

Sensitivity of trichloramine to various rate coefficients

42

Although trichloramine showed sensitivity towards the changes of each coefficient

(shown in Table D-5), the resulting change in concentration never exceeds 2x10-6 M.

Trichloramine is always most sensitive to its formation reaction. It is also sensitive to

monochloramine formation and hydrolysis reactions in the combined region; at (Cl2/N)0

1.2, dichloramine formation, and Reaction 12; and Reaction 12 and 13 at (Cl2/N)0 1.7.

Sensitivity of pH to various rate coefficients

The changes in the values of the rate coefficients had minimal impact on pH. As shown

in Table D-6, all CN are less than 5x10-4.

Conclusions

In general, the model is very sensitive to monochloramine formation and hydrolysis

reactions in the combined region whereas trichloramine formation reactions, Reaction 12,

13, and 14 are more important in transition and breakpoint regions. Dichloramine

formation reaction is shown to be an important reaction at all conditions tested. Under all

initial conditions, the model shows more sensitivity towards acid catalysis reactions, i.e.

monochloramine decomposition reaction, when buffer concentration is high. There are a

few rate coefficients to which no species showed any significant sensitivity. They are k6,

k8 and k9 (when the ratio between them is kept the same), and all the rate coefficients

associated with Reaction 15. Reaction 6, the back reaction of monochloramine

disproportionation is only important when free ammonia concentration is exceedingly

large (Jafvert 1985).

43

4 Data Collection

4.1 Available data from the literature

Data was collected for calibration and validation purposes. Due to the extensive studies

conducted on aqueous chlorine and ammonia reactions, data in the literature was first

reviewed. In accordance with the goal of this study, the typical ranges of parameters used

in the drinking water treatment practice were used as criteria for data selection from the

literature and for the experimental design in the next section. They are initial chlorine

concentration less than 10 mg/L, pH 6.5 to 10, temperature 4 to 35°C, and using

carbonate buffer system.

In his dissertation, Wei (1972) documented series of batch experiments conducted in

breakpoint region, within which three used carbonate buffer system. Saunier (1976)

studied the breakpoint reactions using a plug flow reactor and tap water. Due to the

different mixing condition provided by plug flow reactor and the other constituents (other

than chlorine and ammonia species) introduced by tap water, his data is unsuitable for

this work. The experiments Leao conducted used an initial monochloramine

concentration of 50 to 100 mg/L (Leao 1981), which exceeded the required range here.

Although Jafvert (1985) reported numerous experiments conducted in combined,

transition, and breakpoint regions, phosphate instead of carbonate was used as buffer.

Diyamandoglu (1989) used plug flow reactor and initial chlorine concentration larger

than 20 mg/L, both of which did not conform to the underlying conditions of this study.

Valentine et al. (1998) included monochloramine data for experiments in the combined

region, and the initial conditions coincided with this study. These data were selected and

44

used for calibration. The experimental conditions for the selected data are listed in

Appendix B.

4.2 Experimental procedures and methods

Although Valentine (1998) conducted batch experiments using carbonate as buffer in

combined chlorine region, no data was available for initial pH higher than 8.3 and

(Cl2/N)0 beyond 0.7. In breakpoint region, the initial pH of the selected experiments from

Wei (1972) was around 7. Thus batch experiments were conducted to fill in the gap

between the previously described ranges and the available data from the literature.

A total of six experiments were carried out as listed in Table C-1 (Appendix C).

Experiment 1 to 3 were designed to collect data at (Cl2/N)0 0.95 and at different

temperatures. Experiment 4 to 6 were in transition or breakpoint region. Due to the fast

speed in this region, these experiments were only monitored for 30 minutes, and no

temperature effect was studied. Ionic strength was controlled by adding sodium

perchlorate.

All glassware used in the experiment were soaked over night in about 10 mg/L chlorine

solution (using 5% commercial bleach solution, e.g. Clorox) and then rinsed carefully

with Deionized (DI) Water generated from Millipore Milli-Q system. Chlorine demand

free water was made by first adding 5% (as Chlorine) sodium hypochlorite (from Acros)

into DI water to achieve a concentration of 3 mg/L as Cl2. After sitting overnight, the

water was exposed to sunlight or a UV lamp to remove the remaining free chlorine. This

water was used for the preparation of all reagents. The same sodium hypochlorite from

Acros was used to prepare chlorine stock solution. Ammonium chloride from Fisher was

45

used as the source of ammonia. Other than the sodium hypochlorite, all the chemicals

used are Certified A.C.S. grade. Chlorine stock solution was made right before each

experiment and standardized using primary standard ferrous ammonium sulfate solution.

Experimental procedures for the combined and breakpoint region are different and are

described below.

Procedures for the combined chlorine region

After standardization, the desired amount of chlorine stock solution was added to a

beaker filled with 2 liter chlorine demand free water to achieve the designed initial

concentration. Sodium bicarbonate and sodium perchlorate were added as buffer and

ionic strength control. The value of pH was adjusted to about 9.5 using sodium

hydroxide. Rapid mixing was provided and after 30 seconds the desired amount of

concentrated ammonia stock solution was added into the 2 liter beaker. This sequence

was meant to mimic the full scale practice. Mixing was stopped after another 30 seconds.

The solution was then transported into ten 150 ml amber glass bottles left with no

headspace. At each subsequent sampling time, one bottle was opened and the sample was

tested for free chlorine, monochloramine, dichloramine, and pH.

Procedures for breakpoint region

Ammonia stock solution was added into a 500 ml beaker containing 500 ml Chlorine

demand free water, while chlorine stock solution was added to another beaker with 500

ml chlorine demand free water. Both of these solutions were prepared at double the initial

concentrations as designed. Buffer was then added to each beaker and ionic strength was

increased to 0.01 M. After pH adjustment, under rigorous mixing, the two solutions were

poured into a 1L beaker as quickly as possible. Mixing was stopped after one minute and

46

the beaker was covered to mimic a closed system. Samples were taken from the beaker at

subsequent times using a 100ml volumetric flask for DBP-FAS titration.

Each run was repeated for two times. During the first time, pH and free chlorine were

tested. And during the second, pH, monochloramine and dichloramine were tested.

No attempt was made for determination of trichloramine due to the limited amount of

samples available and the poor reproducibility using DPD method (Pressley, Dolloff et al.

1972; Saunier 1976). Furthermore, under the experimental conditions used in this study,

the concentration of trichloramine is expected to be very low. Nitrate was not monitored

due to time and resource constraints.

Detection methods

The N,N-diethyl-p-phenylenediamine (DPD) method (APHA, AWWA et al. 1998) was

used for determination of the chlorine species. For those experiments in the combined

chlorine region, one titration was carried out to determine monochloramine and

dichloramine. For the other three experiments, where both free chlorine and

monochloramine can be present at a significant concentration at the same time, the

presence of a significant amount of monochloramine will introduce a positive error

during the detection of free chlorine. Thus thioacedamide modification was used (Palin

1978; Palin 1980). Three drops of 0.25% thioacedamide was added immediately after the

sample was transferred into the beaker containing DPD and phosphorus buffer. This

would quench the reaction between monochloramine and DPD to prevent the

interference.

47

pH was measured by using a ThermoOrion 230+ pH meter with a 9107BN probe, which

was calibrated daily.

48

5 Model Calibration and Validation

Most of the reactions listed in Table 2-4 were investigated through kinetic studies or

proposed according to mechanistic basis. Reaction 10, as stated in Chapter 2, was first

included in a model (Leao 1981) to improve the fitting between the predicted value and

the experimental data, which was not based on a solid mechanism. The models, in which

Reaction 10 was part of the reaction scheme, were calibrated to the initial chlorine

concentrations beyond the range that is interested in the study (Leao 1981; Jafvert 1985).

Moreover, during sensitivity analysis, no significant sensitivity was shown towards k10

at all tested conditions. Thus this reaction was excluded from the reaction scheme of this

study. However in order to maintain the consistency throughout the manuscript, the

numbering of the reactions in Table 2-4 was unchanged and the rate coefficient of

Reaction 10 was set to 0, as shown in Table 5-1.

The majorities of the other 21 rate coefficients, which were established through kinetic

experiments, were not calibrated in this study. Only those obtained by data fitting and

listed as “empirical” in Table 5-1 were calibrated, i.e. k5HCO3, k5H2CO3, k12, k13, and k14.

Jafvert (1985) calibrated the Unified Model first in the combined region then in

breakpoint region, claiming that only part of the reactions were important in the

combined region while the rest were important in the breakpoint region. The result of the

sensitivity analysis sustained this approach (See Section 3.2). The model showed

moderate sensitivity towards monochloramine disproportionation reaction only in the

combined region whereas dichloramine decomposition reactions (Reaction 12, 13, 14)

were only of importance in the breakpoint region. Therefore data collected in the

49

combined region, namely the 23 sets of data available in Valentine’s 1998 report and

Experiments 1 through 3 from this study, were used to calibrate k5HCO3 and k5H2CO3.

Then keeping the calibrated values of k5HCO3 and k5H2CO3, k12, k13, and k14 will be

calibrated using 3 datasets from Wei (1972) and Experiments 4 and 5 from this study.

The data in transition region, Experiment 6 from this study, was used for validation of the

model.

Palin (Wei 1972) conducted extensive experiments at low initial ammonia concentration

(3.57x10-5 M, or 0.50 mg/L as N) across a broad range of (Cl2/N)0 (0.2 to 2.4). No initial

pH was reported which hinders the use of these data for calibration or validation

purposes. Nevertheless, the reported final pH can be used to estimate the initial pH.

Qualitative comparison of Palin’s data with model simulation will be shown in Appendix

F.

50

Table 5-1 Updated Reaction Scheme and Rate Coefficients for the Unified Plus Model

No. Reactions Rate expression Rate coefficients Reference for rate coefficients

1 HOCl + NH3 → NH2Cl + H2O k1[HOCl][NH3] k1=2.04x109xexp(-1887/T) M-1s-1 This work 2 NH2Cl + H2O → HOCl + NH3 k2[NH2Cl] k2 = 1.38x108exp(-8800/T) s-1 Morris and Isaac,1983 3 HOCl + NH2Cl → NHCl2 + H2O k3[HOCl][NH2Cl] k3=3.0x105exp(-2010/T) M-1s-1 Morris and Isaac, 1983 4 NHCl2 + H2O → HOCl + NH2Cl k4[NHCl2] k4=6.5x10-7 M-1s-1 Margerum 1978 5 NH2Cl + NH2Cl → NHCl2 + NH3 k5[NH2Cl][NH2Cl] k5 = k5H[H+] + k5HCO3-[HCO3-] + k5H2CO3[H2CO3] Jafvert 1985 k5H=3.78x1010exp(-2169/T)/3600 M-2s-1 Granstrom,1954 k5HCO3-=1.5x1035exp(-22144/T)/3600 M-2s-1 Valentine 1998, empirical k5H2CO3=2.95x1010exp(-4026/T)/3600 M-2s-1 Valentine 1998, empirical




b + 3HClb k10[NH2Cl][NHCl2] k10=0 Excluded in this study 11 HOCl + NHCl2 → NCl3 + H2O k11[HOCl][NHCl2] k11 = k11OH-[OH-] + k11OCl-[OCl-] + k11CO3--[CO3--] Hand and Margerum, 1983


12 NHCl2 + NCl3 + 2H2O → 2HOCl + N2b + 3HClb k12[NHCl2][NCl3][OH-] k12=5.56x1010 M-2s-1 Jafvert 1985, Empirical

13 NH2Cl + NCl3 + H2O → HOCl + N2b + 3HClb k13[NH2Cl][NCl3][OH-] k13=1.39x109 M-2s-1 Jafvert 1985, Empirical

14 NHCl2 + 2HOCl + H2O → NO3- + 5H+ + 4Cl- k14[NHCl2][OCl-] k14=2.31x102 M-1s-1 Jafvert 1985, Empirical




51

5.1 Calibration

Calibration loop was designed in VBA to allow simultaneous calibration of multiple rate

coefficients. For each rate coefficient to be calibrated, a range of values was chosen

carefully after reviewing the results from baseline simulation (see the following

paragraph) and sensitivity analysis. For each calibration dataset, the simulated results

were compared with experimental data by calculating the Root Mean Square Error

(RMSE). At the end of the calibration, for each value combination of the calibrated rate

coefficients, the RMSE of all data sets were added and compared. The value combination

with the least total RMSE value was considered the optimum values, based on which a

smaller range of values was selected for each rate coefficient for the next calibration run.

The same procedures were followed in the combined and breakpoint regions although

different datasets were used in each corresponding region. In the combined region, only

monochloramine data were available from the AWWARF study conducted by Valentine

et al. (1998), and no significant dichloramine was detected during the experiments

conducted in this study. Therefore RMSE was only calculated for monochloramine in

combined region. In breakpoint region, RMSE for free chlorine, monochloramine, and

dichloramine were calculated. Total chlorine was calculated as the summation of these

three species since trichloramine was not expected or measured in either Wei’s

dissertation or this study.

The baseline simulation used the values of the rate coefficients listed in Table 5-1. Before

calibration, the average RMSE of monochloramine for the 26 dataset in the combined

region was 1.89x10-6 M. In the breakpoint region, the average RMSE from 5 datasets for

52

free chlorine, monochloramine, dichloramine and total chlorine were 2.63x10-6 M,

4.51x10-6 M, 3.42x10-6 M, and 5.51x10-6 M respectively.

5.1.1 Calibration in the combined chlorine region

The optimum values of k5HCO3 and k5H2CO3 were found first for 25°C. Then by

calibrating to dataset at different temperatures, the optimum values for frequency factor

and activation energy of both coefficients were determined. The Arrhenius Equation

obtained for k5HCO3 and k5H2CO3 are,

⎟⎠⎞

⎜⎝⎛

×−

××=

⎟⎠⎞

⎜⎝⎛

×−

××= −

Tk

Tk

HCO

HCO

987.133500exp1052.25

987.11000exp1068.85

253

13


Both frequency factor and activation energy of k5HCO3 were significantly less than those

proposed by Valentine (1998). On the other hand, both values for k5H2CO3 were higher

than the values used by Valentine. These adjustments allowed the model to make good

predictions at higher pH, lower buffer concentration, and higher (Cl2/N)0 in the combined

region. The average RMSE after calibration was 1.24x10-6, a 34% improvement over the

baseline condition. As shown in Figure 5-1 to 5-26, the model generally showed a good

fit in the range of the following conditions: (Cl2/N)0 of 0.5 to 0.9, pH of 6.5 – 9.5,

carbonate buffer concentration of 0.001 – 0.01M. At pH 9.5, monochloramine is much

more stable than at lower pH and no significant dichloramine was detected. According to

the model, significant concentration of dichloramine was formed at pH 6.6, yet no data

53

was available to compare with the modeled results. In the following figures, each

increment on the x axis is one day which equals to 86400 seconds.

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M

NH2Cl Data Mono NHCl2 Free Cl2

Figure 5-1 Comparison between model simulation and data (Data source Valentine 1998 Fig 4.1) 25°C, pH 7.64, µ 0.1M, CTCO3 0.004M, (Cl2/N)0 0.7

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M


Figure 5-2 Comparison between model simulation and data (Data source Valentine 1998 Fig 4.1)

25°C, pH 7.6, µ 0.1M, CTCO3 0.004M, (Cl2/N)0 0.7

54

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-06

1.0E-05

1.2E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M


Figure 5-4 Comparison between model simulation and data (Data source Valentine 1998 Fig4.1) 25°C, pH 7.7, µ 0.1M, CTCO3 0.004M, (Cl2/N)0 0.7

55

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



56

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



57

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



58

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



59

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



60

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



61

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



62

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



63

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



64

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M


Figure 5-23 Comparison between model simulation and data (Data source Valentine 1998 Fig4.10)

25°C, pH 8.3, µ 0.1M, CTCO3 0.01M, (Cl2/N)0 0.7

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M


Figure 5-24 Comparison between model simulation and data from Exp1 35°C, pH 9.52, µ 0.01M, CTCO3 0.0009M, (Cl2/N)0 0.9

65

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800 691200Time, s

Con

cent

ratio

n, M



0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 86400 172800 259200 345600 432000 518400 604800Time, s

Con

cent

ratio

n, M


Figure 5-26 Comparison between model simulation and data from Exp3

4°C, pH 9.52, µ 0.01M, CTCO3 0.0009M, (Cl2/N)0 0.9

66

5.1.2 Calibration in breakpoint region

The redox reactions in breakpoint region were the least studied among the reactions listed

in Table 5-1. Nitrogen gas is believed to be the major product (Palin 1950; Pressley,

Dolloff et al. 1972) during breakpoint chlorination which would lead to the breakpoint

location at (Cl2/N)0 1.5. Other nitrogenous oxidation products, such as N2O, NO, and

NO3-, may also form which will cause breakpoint to shift beyond (Cl2/N)0 1.5.

Nonetheless nitrate was the only products other than nitrogen gas which was

experimentally detected (Pressley, Dolloff et al. 1972).

Palin (1950) reported breakpoint to be between 1.62 and 1.64 at pH 7 to 8, 1.68 at pH 9

and 1.87 at pH 6 for a contact time of one day. With the initial ammonia nitrogen ranging

from 4.7x10-5 to 1.4x10-4 M, the amount of nitrate formed was reported to increase with

increasing (Cl2/N)0 (Palin 1950). Pressley (1972) observed breakpoint location to be

approximately 1.58 at pH 6-7, and between 1.58 and 1.78 at pH 8, using 20 mg/L initial

ammonia concentration. Pressley (1972) also reported that the formation of NO3- after 2

hours at the breakpoint ((Cl2/N)0 around 1.6) decreased from about 2.0 mg/l at pH 8.0 to

0.3 mg/l at pH 5-6.

In a more resent study, Phillip and Diyamandoglu (2000) studied the kinetics of nitrate

formation in breakpoint region at 25°C under the following conditions, initial ammonia

concentration 0.25 to 1 mg/L (0.018 – 0.071 mM), (Cl2/N)0 1.7 to 3.3, pH 6.6 to 8.6.

Although no detailed mechanism was substantiated, it was reported that nitrate formation

experienced an initial fast increase before a plateau was reached as free chlorine

concentration became steady. The initial rate of nitrate formation increased with

67

decreasing pH at a constant (Cl2/N)0 of 2.1. And when the initial pH and ammonia

concentration were constant, nitrate formation increased with increasing (Cl2/N)0. It also

increased as the initial ammonia concentration increased at constant initial pH and

(Cl2/N)0. At 25°C and pH 7.6-7.71, under the different initial ammonia and molar ratio

studied, nitrate nitrogen made up from 11% to 20%, or an average of 16%, of the initial

ammonia nitrogen concentration at the end of 60 minutes. Nitrite was not observed under

any of the experimental conditions. Nitrogen gas was not measured.

Nitrate formation in the combined region was also studied. Vikesland et al. (1998)

conducted mass and redox balance at (Cl2/N)0 0.7 and 25°C, aiming to elucidate the

effect of natural organic matter (NOM) on monochloramine decomposition. The

inorganic products of the monochloramine decomposition were measured, i.e. chloride,

nitrate, nitrite, ammonia, and nitrogen gas, and compared to the amount of

monochloramine loss. Despite the fact that the average nitrogen recovery was only 97%

after 9 days, only an average level of 0.9% was recovered as nitrate. Ammonia

production from the decomposition process corresponded to 47.7% of monochloramine

nitrogen on average, while nitrogen gas corresponded to 49%. No nitrite was ever

detected. This is consistent with Leao’s (Leao 1981) finding that in the combined region

the molar ratio of chlorine reduced to ammonia oxidized after 15 days was generally

between 1.55 and 1.65. With the presence of NOM, the average values after 9 days were

70% total nitrogen recovery with 10% as nitrogen gas, 7.8% as nitrate, and 52.2% as

ammonia (Vikesland, Ozekin et al. 1998). The low recovery rate was attributed to the

incorporation of N(III) into the NOM structure (Vikesland, Ozekin et al. 1998). The

increase in nitrate production and decrease in nitrogen gas production was speculated to

68

be due to a product speciation shift toward the formation of nitrate relative to nitrogen

gas when NOM is present (Vikesland, Ozekin et al. 1998).

All of the above were conducted with phosphate buffer system. They were given

qualitative consideration during calibration.

The rate coefficients of Reaction 12, 13, and 14 were calibrated simultaneously. Reaction

14 is the only reaction which accounts for nitrate formation. The values of k12, k13, and

k14 determine the location of the breakpoint.

When using data from Wei’s study, special consideration was given to the fact that final

pH was higher than initial pH by 0.1 to 0.2 units. Wei speculated that this may be due to

the loss of carbon dioxide to the atmosphere through continuous mixing (Wei 1972).

Calculation was conducted for carbonate equilibrium at the initial pH and total carbonate

concentration used by Wei. It was indeed oversaturated. The baseline simulation results

before calibration of k12, k13, and k14 were reviewed for Wei’s experiments. At high

initial ammonia concentration, during the first 10 minutes of the reaction, the peak of

dichloramine was greatly under predicted while monochloramine as well as free chlorine

were over predicted. On the other hand, after 20 minutes, monochloramine and

dichloramine concentrations were over predicted while free chlorine was under predicted.

As Wei (1972) pointed out, the resurgence of free chlorine observed in carbonate buffer

was not observed in phosphate buffer and could be due to the increase of pH. This is

believed to be reasonable because dichloramine decomposition reactions (Reaction 7 and

12) are both base catalytic reactions, which would lead to faster dichloramine

decomposition and at the same time more free chlorine as the product. Therefore it is

likely that the pH change reported by Wei had no significant impact during the first 10

69

minutes of the reaction. Yet the later data points were impacted. This led to assigning

weight coefficients to different data points when RMSE was calculated during calibration.

The data points collected before 10 minutes were given twice the weight as those

collected later during each experiment from Wei (1972).

The calibrated values for these coefficients are k12 1x1014 M-2s-1, k13 1x106 M-2s-1, and

k14 66 M-1s-1 as listed in Table 5-2. The average RMSE for free chlorine,

monochloramine, dichloramine, and total chlorine were 2.61x10-6 M, 3.57x10-6 M,

4.1x10-6 M, and 4.8x10-6 M respectively. As shown in Figure 5-27 and 5-28, the model

was able to have reasonable prediction at pH 9.5 where no significant concentration of

dichloramine was present. Monochloramine concentration remains significant even after

breakpoint reaction at pH of 9.5. However at pH 7, the model did not seem to capture the

trend at the beginning of the breakpoint reaction. In Figure 5-29 to 5-31, at pH 7,

monochloramine as well as free chlorine concentrations were over predicted. At high

initial ammonia concentration, dichloramine peak was greatly under predicted although

the prediction was good at low initial concentration. On the other hand the dissipation of

dichloramine was reasonably estimated by the model at high initial ammonia

concentration but under estimated at low initial ammonia concentration.

This “opposite” trend led to a search for the coefficients which had opposite effect on

dichloramine at the first 100 seconds and at 30 minutes. k13 satisfied this requirement

however the sensitivity the reaction system showed towards it was too small to improve

the outcome even after changing its value to 6 orders of magnitude larger.

70

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 300 600 900 1200 1500 1800 2100 2400Time, s

Con

cent

ratio

n, M

NH2Cl DataMono NHCl2 DataDiFree Cl2 DataFree Total Data Total


22°C, pH 9.54, µ 0.01M, CTCO3 0.0009M, (Cl2/N)0 1.7

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 300 600 900 1200 1500 1800 2100 2400Time, s

Con

cent

ratio

n, M



21.5°C, pH 9.53, µ 0.01M, CTCO3 0.0009M, (Cl2/N)0 2.0

71

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

3.5E-05

0 300 600 900 1200 1500 1800 2100 2400Time, s

Con

cent

ratio

n, M


Figure 5-29 Comparison between model simulation and data from Wei Exp 4-25

20°C, pH 7.04, µ 0.005M, CTCO3 0.005M, (Cl2/N)0 1.7

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

0 300 600 900 1200 1500 1800 2100 2400Time, s

Con

cent

ratio

n, M



20°C, pH 7.05, µ 0.01M, CTCO3 0.01M, (Cl2/N)0 1.7

72

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

1.4E-04

0 300 600 900 1200 1500 1800 2100 2400Time, s

Con

cent

ratio

n, M



20°C, pH 7.16, µ 0.01M, CTCO3 0.01M, (Cl2/N)0 1.7

In his dissertation, Wei (1972) concluded that the higher the initial ammonia

concentration, the sooner the peak of dichloramine would occur and the larger the

magnitude of the peak would be. Consequently, the rate of decrease for monochloramine

and dichloramine would also increase. As depicted in Figure 5-32, the simulated

dichloramine concentration normalized by initial ammonia concentration was compared

for the three experiments from Wei. The model captured the impact of initial ammonia

concentration on the occurrence of the peaks and the decomposition. But the magnitude

of the peaks was greatly under predicted.

In Figure 5-30 and 5-31, the predicted chlorine concentration approached a steady

concentration at the end of 30 minutes. When the duration of the simulation was extended,

free chlorine concentration started to increase very slightly at about 2 hours for

Experiment 4-27 and after 3 hours for Experiment 4-26. This resurgence pattern was not

as pronounced as what Wei observed and the rate of this resurgence was much slower.

73

Wei (1972) speculated that the slight increase in pH might cause this observed distinct

resurgence in carbonate buffer.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 300 600 900 1200 1500 1800 2100 2400Time, s

Dic

hlor

amin

e/N

0

Data Wei Exp 4-25 Data Wei Exp 4-26 Data Wei Exp 4-27Wei Exp 4-25 Wei Exp 4-26 Wei Exp 4-27

Figure 5-32 Comparison between model simulation and data from Wei 1972 on the impact of

initial ammonia concentration on dichloramine concentration

Trichloramine was not measured due to its insignificant presence at the experimental

conditions used herein (Hand and Margerum 1983). Nitrate was not measured either in

this study. The simulated concentration of these two species at different pH and initial

chlorine to ammonia molar ratios are summarized in the following two figures. The

formation of both species increase with increasing initial (Cl2/N)0. Nitrate formation was

higher at higher pH values while trichloramine was more significant at lower pH. The

initial ammonia concentration used here was 7x10-5 M. Due to the speculative nature of

Reaction 12, 13, and 14, no quantitative comparison was made. However, the simulated

results conform well to the trend reported by other researchers (Palin 1950; Pressley,

Dolloff et al. 1972; Jafvert 1985).

74

0.0E+00

5.0E-03

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1

Initial (Cl2/N)0

NO

3-/N

0

pH9pH8pH7pH6

Figure 5-33 Model simulated formation of nitrate as a fraction of initial ammonia at different

(Cl2/N)0 at 1 hour

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-06

1.0E-05

1.2E-05

1.4E-05

1.6E-05

1.8E-05

2.0E-05

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1

Initial (Cl2/N)0

NC

l3/N

0

pH9pH8pH7pH6

Figure 5-34 Model simulated formation of trichloramine as a fraction of initial ammonia at

different (Cl2/N)0 at 1 hours

In the breakpoint region, dichloramine is the most important species in this dynamic

reaction system. However all the important reactions related to dichloramine

decomposition in this reaction scheme are kinetically based speculations and their rate

75

coefficients were all obtained through data fitting. These reactions are the redox reaction

scheme when no significant free chlorine is present (Reaction 7, 8, 9); the redox reaction

scheme when free chlorine is present (Reaction 12, 13), and nitrate formation reaction

(Reaction 14). As more data using carbonate buffer system becomes available, further

adjustment of these coefficients may improve the performance of the model.

Although the beginning of the breakpoint reaction was not well captured by the calibrated

model, it is not believed to be important for field practice. In drinking water treatment

plant, depending on its size, water usually stays in the clear well for about half an hour to

hours before entering the transmission line. Thus it is the later stage when the reaction

system approaches equilibrium which is of real concern.

The final values for the rate coefficients are listed in Table 5-2.

5.2 Validation

As shown in Figure 5-35, at pH 9.5, the calibrated model tends to under predict

monochloramine concentration, and over predicts free chlorine concentration. This

suggests that the value of k7 might be too large. From Figure 5-27, 5-28, and 5-35, it can

be concluded that at pH 9.5, monochloramine is very stable even in breakpoint and

transition regions.

Palin had conducted extensive experiments using carbonate buffer (Wei 1972) and

collected data at 10 minutes, 2 hours, and 1 day of each experiment. These data were

generated in the 1950’s, which may be subject to the limitations in experimental

technique as well as detection methods. Nevertheless, due to the scarcity of data in

carbonate buffer with initial chlorine and ammonia concentrations close to those in the

76

field practice, these data were used to compare qualitatively with the simulated results

from The Unified Plus Model. In the breakpoint and transition regions, only the data

point at 10 minutes and 2 hours were used for this comparison. The results are presented

in Appendix F. As shown in the figures of Appendix F, the goodness of fit between

Palin’s data and the modeled results are quite scattered. This could be due to the reasons

mentioned above or the inaccuracy in the estimated initial pH values.

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 300 600 900 1200 1500 1800 2100 2400

Time, s

Con

cent

ratio

n, M

NH2Cl DataMono NHCl2 DataDi

Free Cl2 DataFree Total Cl2 Data Total


77

Table 5-2 Final Reaction Scheme and Rate Coefficients for the Unified Plus Model No. Reactions Rate Expression Rate coefficients Reference 1 HOCl + NH3 → NH2Cl + H2O k1[HOCl][NH3] k1=2.04x109xexp(-1887/T) M-1s-1 This work 2 NH2Cl + H2O → HOCl + NH3 k2[NH2Cl] k2 = 1.38x108exp(-8800/T) s-1 Morris and Isaac,1983 3 HOCl + NH2Cl → NHCl2 + H2O k3[HOCl][NH2Cl] k3=3.0x105exp(-2010/T) M-1s-1 Morris and Isaac, 1983 4 NHCl2 + H2O → HOCl + NH2Cl k4[NHCl2] k4=6.5x10-7 M-1s-1 Margerum 1978 5 NH2Cl + NH2Cl → NHCl2 + NH3 k5[NH2Cl][NH2Cl] k5 = k5H[H+] + k5HCO3-[HCO3-] + k5H2CO3[H2CO3] Jafvert 1985 k5H=3.78x1010exp(-2169/T)/3600 M-2s-1 Granstrom,1954 k5HCO3-=0.87exp(-503/T)/3600 M-2s-1 This work k5H2CO3=2.52x1025exp(-16860/T)/3600 M-2s-1 This work




b + 3HClb k10[NH2Cl][NHCl2] k10=0 Excluded in this study 11 HOCl + NHCl2 → NCl3 + H2O k11[HOCl][NHCl2] k11 = k11OH-[OH-] + k11OCl-[OCl-] + k11CO3--[CO3--] Hand and Margerum, 1983


12 NHCl2 + NCl3 + 2H2O → 2HOCl + N2b + 3HClb k12[NHCl2][NCl3][OH-] k12=1.00x1014 M-2s-1 This work

13 NH2Cl + NCl3 + H2O → HOCl + N2b + 3HClb k13[NH2Cl][NCl3][OH-] k13=1.00x106 M-2s-1 This work

14 NHCl2 + 2HOCl + H2O → NO3- + 5H+ + 4Cl- k14[NHCl2][OCl-] k14=66 M-1s-1 This work




78

6 Case Studies

The Unified Plus Model is a comprehensive model which includes the reactions in both

combined and breakpoint regions, and has been calibrated to the following ranges, initial

chlorine concentration less than 10 mg/L, pH 6.5 to 10, temperature 4 to 35°C, and the

use of carbonate buffer system. This model can be used for different applications with

some moderate modifications. In this chapter, a few of these applications are presented.

6.1 Breakpoint curve

Traditionally, breakpoint curve is plotting chlorine concentration versus chlorine to

ammonia nitrogen weight or molar ratio. It shows the formation of chloramines and redox

of ammonia nitrogen. At a constant initial ammonia concentration, as chlorine dose

increases, the residual chlorine concentration rises to a maximum at chlorine to ammonia

nitrogen molar ratio of about 1, and then falls to a minimum at a molar ratio of 1.5 to 2.0,

depending on the initial pH and reaction time. The location of the minimum chlorine

residual is called the “breakpoint”. After this point, chlorine residual, primarily in the

form of free chlorine, starts to increase as chlorine to ammonia nitrogen ratio increases.

Jafvert (1985) used the Unified Model to generate the three dimensional breakpoint curve

surface which also included the time dimension.

Jar test device is usually used for generating data to create breakpoint curve. The same

amount of ammonia is dosed into a series of beakers containing equal volume of water.

Subsequently, with sufficient mixing, a different amount of free chlorine is added to each

beaker to achieve the desired chlorine to ammonia ratio. Later, samples are drawn from

each beaker to determine the concentrations of each chlorine species.

79

A more informative way of presenting breakpoint curve is to normalize the y axis to

initial free ammonia concentration and to use chlorine to ammonia nitrogen molar ratio as

the x axis (Wei 1972). Using this plotting technique, the ideal chlorine residual peak

should be at (1, 1), which allows easy diagnosis of any distortion. Moreover this

facilitates the comparison of breakpoint curves generated using different initial ammonia

concentrations.

From the kinetic data shown in Figure 5-29, 5-30, and 5-31 in the previous section, at

neutral pH, the reaction system is dynamic in the first 10 minutes. It is after 30 minutes

that the concentrations of all species become relatively stable, and the reaction system is

approaching equilibrium. At this later stage the breakpoint curve is better defined and can

clearly depict the outcome of this reaction system.

A loop was added to the Unified Plus Model to allow continuous simulation at a set of

different initial (Cl2/N)0. The simulated kinetic results at 45 minutes were saved after

each simulation at one specific (Cl2/N)0. A breakpoint curve was then generated using the

saved set of concentrations at 45 minutes and the corresponding initial (Cl2/N)0.

Figure 6-1 through 6- 4 showe the normalized breakpoint curve predicted by the Unified

Plus Model at different initial pH. At pH 9, monochloramine is very stable. Its peak is

very close to the theoretical value of (1, 1) in the plot and its concentration at breakpoint

remains significant even after 45 minutes. Dichloramine formation is much slower than

its decomposition thus no significant dichloramine is present at this pH. The breakpoint at

this pH is at (Cl2/N)0 1.65. At pH 8, monochloramine peak is slightly lower than the

theoretical position (1, 1). Dichloramine is formed and then decomposes so that no

significant presence of dichloramine is shown in Figure 6-2. Free chlorine starts

80

increasing after (Cl2/N)0 is larger than 1.5 and is the dominant species after the

breakpoint which is at 1.6. At pH 7, dichloramine is detectable before (Cl2/N)0 of 1 and

its concentration is most significant at (Cl2/N)0 1.4. The peak of monochloramine is only

at 0.9 due to the presence of dichloramine. As a result, the peak of total chlorine shifts to

the right and the magnitude of the peak is lower than 1, indicating loss due to redox

reactions. The simulated breakpoint location is at 1.625 at pH 7 which implies a relatively

higher production of nitrate compared to at pH 8. At pH 6, dichloramine formation is

much faster than its decomposition and its concentration peaks at (Cl2/N)0 1.8. This

causes instability of monochloramine and its peak is only at 0.65 instead of 0.9 at pH 7.

Breakpoint at pH 6 is at (Cl2/N)0 1.9, due to the persistent presence of dichloramine. No

significant trichloramine concentration is predicted at any of these pH levels.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

Dosing Molar Ratio (Cl2/N)o

Mea

sure

d M

olar

Cl2

/No

Mono Di Free Cl2 Tri Total

Figure 6-1 Simulated breakpoint curve after 45 minutes at initial pH 9

25°C, N0 7x10-5 M, CTCO3 0.01M

81

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6


Mea

sure

d M

olar

Cl2

/No



25°C, , N0 7x10-5 M, CTCO3 0.01M

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6


Mea

sure

d M

olar

Cl2

/No


Figure 6-3 Simulated breakpoint curve after 45 minutes at , initial pH 7

25°C, N0 7x10-5 M, CTCO3 0.01M

82

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6


Mea

sure

d M

olar

Cl2

/No



25°C, , N0 7x10-5 M, CTCO3 0.01M

As shown in the above four figures, the Unified Plus Model can be used to generate

breakpoint curves at different initial conditions such as pH, buffer concentration,

temperature, etc. After normalizing the y axis by initial ammonia concentration and

having (Cl2/N)0 instead of the weight ratio as the x axis, the plot allows convenient and

clear comparison among breakpoint curves generated at different initial conditions.

6.2 Mixing effect

One of the underlying assumptions of the Unified Plus Model is uniform mixing. In other

words, initial (Cl2/N)0 prevails at all parts of the batch reactor. If mixing is insufficient or

not uniform, unexpected molar ratio might exist in different parts of the reactor, which

would lead to undesired products. A recent study by Jain (2007) evaluated the effect of

mixing on chloramination process using breakpoint curve. Jar test device was used to

83

collect data at (Cl2/N)0 of 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1,75, 2, and 4. Different levels of

mixing were provided, namely at 50, 150, and 200 rpm. As shown in Figure 6-5 when

comparing the breakpoint curves obtained at 200 and 50 rpm at neutral pH, the

occurrence of the peak monochloramine concentration decrease from (Cl2/N)0 1 at 200

rpm to (Cl2/N)0 0.75 at 50 rpm, and the magnitude of the peak also decreased from 0.92

to 0.75 as the mixing speed decreased. Meanwhile breakpoint shifted from (Cl2/N)0 1.75

at 200 rpm to (Cl2/N)0 1.25 at 50 rpm. Jain concluded that insufficient mixing would

cause breakpoint to shift towards the origin (Jain 2007). Similar results were reported in a

Japanese study (Yamamoto, Fukushima et al. 1990) using sea water.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

Dosing Molar Ratio (Cl2/N)0

Mea

sure

d M

olar

Cl2

/N0

50 rpm

200 rpm

Figure 6-5 Breakpoint curve of total chlorine concentration (Data source: Jain 2007)

10°C, initial pH 7, N0 7x10-5 M, CTCO3 0.012M

The breakpoint curve generated by the Unified Plus Model is the outcome at uniform

mixing condition. When compared to experimentally generated breakpoint curve, any

deviation caused by insufficient mixing can be clearly shown. Figure 6-6 compares the

84

model simulation and Jain’s data using 200rpm. The occurrence of the monochloramine

peak agrees between the simulated value and data at (Cl2/N)0 1. Nevertheless, the

magnitudes of the two monochloramine peaks differ by about 0.1 units on the y-axis. The

model predicted significant dichloramine residual at 45 minutes while no dichloramine

was detected throughout Jain’s experiment. This causes the modeled monochloramine

peak to be less than the observed. The magnitude of the simulated total chlorine peak is

the same as that of the observed total chlorine peak, yet the occurrence of the peak is

skewed by the significant presence of the simulated dichloramine. This discrepancy of

dichloramine could be due to the fact that the model simulates a closed system while

Jain’s experiment was conducted in open atmosphere. The high initial total carbonate

buffer concentration used in Jain’s experiments led to an oversaturated solution with

respect to atmospheric CO2 at the reported initial pH. Although no other pH data was

reported, it is expected that during the process of reaching equilibrium, the system pH

may increase as the experiment proceeded. This could lead to a faster decomposition of

dichloramine.

Due to the discrete (Cl2/N)0 used during the experiment (Jain 2007), no data was available

between (Cl2/N)0 1.5 and 1.75. Although at (Cl2/N)0 1.75, data showed the lowest total

chlorine residual concentration, the actual breakpoint could fall between (Cl2/N)0 1.5 and

1.75. The modeled breakpoint is at 1.6 which conforms to this observed range.

85

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

Dosing Molar Ratio (Cl2/N)0

Mea

sure

d M

olar

Cl2

/N0

NH2Cl NHCl2 Free Chlorine NCl3 Total ChlorineData Mono Data Di Data Free Data Tri Data Total

Figure 6-6 Comparison between simulated breakpoint curve and data (Data source: Jain 2007)

10°C, pH 7, N0 7x10-5 M, CTCO3 0.012M

More experiments using higher rpm may be necessary in this case in order to determine if

200 rpm can provide sufficient mixing or not. If the peak of monochloramine generated

at a higher rpm remains at the same magnitude as the one generated at 200 rpm, then 200

rpm would be likely to provide sufficient mixing at this initial condition.

Saunier (1976) observed a breakpoint lower than (Cl2/N)0 1.5 when plug flow reactor was

used. He attributed the cause to the difference in mechanism in the oxidation reduction

caused by the intensive mixing in the plug flow reactor. In light of these works

(Yamamoto, Fukushima et al. 1990; Jain 2007) on mixing effect using breakpoint curve,

it seems that it might be the non-uniform mixing in the plug flow reactor which caused

the low observed breakpoint location.

86

6.3 Open system

During the preliminary stage of this study, jar test device was used to conduct kinetic

experiments. The mixer was left on for 15minutes to provide sufficient mixing during the

course of the experiment. With a initial pH of 9 and total carbonate buffer of 9x10-4 M,

the pH experienced a sharp drop of 2 units in 15min. Consequently, monochloramine loss

was accelerated substantially. This phenomenon prompted the question that if the Unified

Plus Model can estimate the effect of open system on chloramine chemistry. Thus an

extension of the model incorporating the impact of open system was developed.

In full scale chloramination process, water is under vigorous mixing at the injection point

of chlorine and ammonia, and then sent to the clear well before it leaves the treatment

plant. Once the water enters the transmission pipe, the environment is a closed system.

Thus the only period of time that water is exposed to the atmosphere is after secondary

disinfection till the end of the clear well. The absorption and desorption rates of

atmospheric CO2 in water is a function of CO2 partial pressure, temperature, pH, means

of mixing, and degree of mixing. Surface to volume ratio is also important. Limited

information was found in the literature on CO2 absorption/desorption rate in fresh water

between pH 6 and 10. A Japanese article (Kazuyuk, Yasuhiro et al. 1998) documented

the absorption rate (2.4x10-3 s-1) and desorption rate (4.5x10-3 s-1) at pH 1-4 using diffuser

to introduce CO2 and N2. These are not suitable for this study since CO2 absorption and

desorption are not likely to be first order where no vigorous agitation or air diffuser are

present.

Due to a lack of the appropriate rate coefficient for CO2 adsorption and desorption, the

assumption was made to let the system reach open system equilibrium instantaneously at

87

the start of the reactions, and then go back to close system with only chloramine

chemistry taking place. If any exchange of CO2 with the atmosphere happens during full

scale operation, this assumption would be the worst case scenario.

Under open system equilibrium,

KH = 10-1.5

PCO2 = 385 ppm = 10-3.41 atm (March, 2008)

[H2CO3*] = KH*PCO2 = 1x10-4.91 M

KH – Henry’s constant PCO2 – partial pressure of CO2

[H2CO3*] – total aqueous carbon dioxide and carbonic acid

At equilibrium [H2CO3*] will be constant, and the total carbonate concentration is

calculated as,

CTCO3 = [H2CO3*] / α0

α0 – ionization fraction of carbonic acid

Alkalinity is conservative and should stay the same before and after the equilibrium is

reached. Thus the value of pH at equilibrium can be calculated using the alkalinity before

the equilibrium.

Using the specified initial pH and CTCO3, pH and CTCO3 under carbonate species

equilibrium were calculated and subsequently used by the Unified Plus Model to simulate

reactions between aqueous chlorine and ammonia.

The following figures depict the impact of open system on monochloramine stability as

well as pH. Figure 6-7 and 6-8 show the comparison between model simulation and one

88

of the experiments from Valentine (1998). At the initial pH of 8.3 and total carbonate

concentration of 0.04M, the carbonic acid concentration was over saturated under the

open system equilibrium. Thus after the equilibrium was reached, the value of pH

increased and total carbonate concentration decreased. As a result, monochloramine was

more stable under open system condition as shown in Figure 6-7. Figure 6-9 and 6-10

show the comparison between model simulation and another experimental dataset with

the same total buffer concentration at 0.04M but a lower initial pH, 6.5. The impact of

open system equilibrium showed the same trend as in the previous case but more

profound in magnitude at this initial pH. As illustrated in Figure 6-11 and 6-12, at initial

pH 9 and total carbonate concentration of 0.009 M, carbonic acid concentration was

under saturated. Therefore after reaching open system equilibrium, pH plummeted almost

2 units and total carbonate concentration increased. Monochloramine loss was greatly

accelerated and dichloramine was formed.

Using the Unified Plus Model, under the assumption for the worst case scenario, the

impact of open system on monochloramine chemistry can be clearly demonstrated.

89

0.E+00

1.E-05

2.E-05

3.E-05

4.E-05

5.E-05

6.E-05

0 86400 172800 259200 345600 432000 518400 604800 691200

Time, s

Chl

orin

e sp

ecie

s co

ncen

tratio

n, M

Open systemClosed system

Figure 6-7 The impact of open system on monochloramine stability 25°C, pH 8.31, µ 0.1M,

CTCO3 0.004M, (Cl2/N)0 0.5 (Data source: Valentine 1998 Fig 4.6)

6

6.5

7

7.5

8

8.5

9

0 86400 172800 259200 345600 432000 518400 604800 691200

Time, s

pH


Figure 6-8 The impact of open system on pH 25°C, pH 8.31, µ 0.1M, CTCO3 0.004M, (Cl2/N)0 0.5

(Data source: Valentine 1998 Fig 4.6)

90

0.E+00

1.E-05

2.E-05

3.E-05

4.E-05

5.E-05

6.E-05

0 86400 172800 259200 345600 432000 518400 604800 691200

Time, s

Chl

orin

e sp

ecie

s, M


Figure 6-9 Impact of open system on monochloramine stability 25°C, pH 6.55, µ 0.05M, CTCO3

0.004M, (Cl2/N)0 0.7 (Data source: Valentine 1998 Fig 4.2)

0

1

2

3

4

5

6

7

8

9

0 86400 172800 259200 345600 432000 518400 604800 691200

Time, s

pH

Open systemClosed System

Figure 6-10 Impact of open system on pH 25°C, pH 6.55, µ 0.05M, CTCO3 0.004M, (Cl2/N)0 0.7

(Data source: Valentine 1998 Fig 4.2)

91

0.E+00

1.E-05

2.E-05

3.E-05

4.E-05

5.E-05

6.E-05

0 86400 172800 259200 345600 432000 518400 604800 691200

Time, s

Chl

orin

e sp

ecie

s, M

Open system

Closed system

Figure 6-11 Impact of open system on monochloramine stability Exp2 22°C, pH 9.57, µ 0.01M,

CTCO3 0.0009M, (Cl2/N)0 0.9

0

2

4

6

8

10

12

0 86400 172800 259200 345600 432000 518400 604800 691200

Time, s

pH


Figure 6-12 Impact of open system on pH 22°C, pH 9.57, µ 0.01M, CTCO3 0.0009M, (Cl2/N)0 0.9

Exp2

92

6.4 Switching disinfectant

Chloramine is a weaker oxidant compared to free chlorine, which makes it preferable in

order to lower DBP formation and provide more stable residual disinfectant in the

distribution system. The chlorine to ammonia molar ratio, which is usually difficult to

maintain, is a critical factor during full scale operation of chloramination. If this ratio is

less than 1, free excess ammonia that enters the distribution system will cause

nitrification, which is usually accompanied by proliferation of heterotrophic bacteria.

Some water utilities temporally switch to free chlorine from chloramine to control

nitrification and bacteria growth in their distribution systems (Odell et al 1996). During

this switch, the very front of the chlorinated water is mixed with chloraminated water

through diffusion and dispersion, and a wide range of chlorine to ammonia ratios can be

expected. Where the ratio reaches the breakpoint, very little disinfection residual is left,

leaving the distribution system susceptible to bacteria growth before the incoming

chlorinated water flushes through the entire system. When returning to chloramination

from short term chlorination, similar phenomena are expected.

In the State of North Carolina, all utilities employing chloramination are mandated to

switch to free chlorine for one month a year (Ferguson et al, 2005). Ferguson et al

studied the impact of the temporary switch to water quality for the City of Durham

(2005). One of the objectives of the study was to measure the extent and duration of the

breakpoint phenomenon caused by the switch from chloramine to free chlorine and,

subsequently, from free chlorine to chloramine. At a fixed location in the distribution

system, continuous total chlorine monitors was used to continuously monitor the change

93

in residual disinfectant before, during and after the switch. The following two figures

depict the breakpoint phenomenon observed during this switch.

Figure 6-13 Breakpoint phenomenon observed during the switch from chloramine to free

chlorine (Ferguson, DiGiano et al. 2005)

Figure 6-14 Breakpoint phenomenon observed during the switch from free chlorine to

chloramine (Ferguson, DiGiano et al. 2005)

94

Covering the reactions in both combined and breakpoint regions, Unified Plus Model is

used in the attempt to reproduce this breakpoint phenomenon during the switching of

disinfectant, i.e. between chloramine and chlorine. In the following section, the model

development for this case study is described. A and B are used to represent free chlorine

and monochloramine respectively for simplicity and clarity. Ca and Cb are used as the

target concentrations of each corresponding disinfectant.

As mentioned before, when B is switched to A, through dispersion and diffusion A and B

are mixed to different extents throughout the mixing front. Assuming this mixing front is

comprised of many small equal length/volume segments, within which uniform mixing is

achieved. A fraction fx is assigned as the fraction of A in one of these segments.

Consequently, (1-fx) represents the fraction of B in the same segment. If a fixed point in

the distribution system is selected as the monitoring site, before the mixing front

approaches this point, or until right before the first segment with any trace of A gets to

the monitoring site, fx is zero and B should be the only disinfectant observed. The time,

when the first segment containing A arrives, is defined as time zero, at which A and B in

all following segments start being mixed at the corresponding fx. When the mixing front

approaches the monitoring site, the very first segment, segment No.1 would have a very

small fx, fx1, and during the process of passing through the monitoring site, the reactions

in the Unified Plus Model will take place using Cafx1 and Cb(1-fx1) as the initial

concentrations for A and B. The time when segment No.1 completely passes through the

monitoring site is referred to as t1. At the end of t1, segment No.2 arrives at the

monitoring site with a slightly larger fx than segment No.1, fx2. However, the

concentrations observed at the monitoring site is not simply Cafx2 and Cb(1-fx2), but the

95

resulted concentrations after t1 using Cafx2 and Cb(1-fx2) as the initial conditions at time

zero. Same applies to each of the following segments. Segment No.3 starts reaction at

time zero with the initial condition of Cafx3 and Cb(1-fx3). When it arrives to the

monitoring site, the observed concentration will be (t1+t2) after the reaction started. After

the very last segment containing the least bit of B passes the monitoring site, the observed

disinfectant will be solely A at Ca.

The values for input parameters are listed in Table 6-1. Most of the values are based on

the Durham 2006 Water Quality Report (2006). The temperature used was the average

temperature of March in Durham, NC. Ionic strength is calculated based on the reported

specific conductivity using the following formula (Snoeyink and Jenkins 1980).

μ=1.6x 10-5 x specific conductance (umho/cm)

Table 6-1 Initial Condition Used for Simulation of Switching Disinfectant

Temp, °C 10 Initial pH 8 Ionic Strength, M 2.7x10-3 Buffer CTCO3, M 5x10-4 Target Free Chlorine, M 2.1x10-5 (1.5 mg/L) Initial Monochloramine, M 4.93x10-5 (3.5 mg/L) Mixing segment length, s 100 fx 0.002

The simulated total chlorine concentration is shown in Figure 6-15 and 6-16. The model

successfully reproduced the breakpoint phenomenon and its duration during the switching

of disinfectant. As expected, the simulated patterns are much sharper than field data in

Fig. 6-13 and 6-14. This may be due to the underlining assumptions of uniform mixing in

each segment and uniform length for each segment. The combination of mixing segment

length and the fx represent the transport characteristic in the distribution system, which is

96

largely site specific. Therefore in order to make predictions, this model has to be

incorporated with a transport model such as EPANET which can predict flow condition

in the pipe.

Other similar applications would be disinfection conversion from free chlorine to

monochloramine, which a lot of utilities are considering as a means to comply with the

upcoming second stage DBP rule. Or in other cases, some communities purchase water

from two water utilities using these two different disinfectants. This can be potentially

dangerous, because as the two waters mix, depending on pH and the concentration and

volume ratio, there might be only very limited disinfection residual left in the distribution

system.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Time, days

conc

., m

g/L

as C

l2

1.1 days

Figure 6-15 Breakpoint phenomenon during switch from chloramine to chlorine simulated by

Unified Plus Model 3.4 mg/L monochloramine to 1.5 mg/L free chlorine, 10°C, pH 8

97

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Time, days

conc

., m

g/L

as C

l2

1.2 days

Figure 6-16 Breakpoint phenomenon during switch from free chlorine to monochloramine

simulated by Unified Plus Model 1.5 mg/L free chlorine to 3.4 mg/L monochloramine, 10°C, pH 8

6.5 Natural Organic Matter (NOM)

During full scale treatment, NOM present in natural water reduces monochloramine and

accelerates its decay. In order for a model to be able to predict disinfectant loss in a full

scale system, the effect of NOM must be considered. Duirk et al. (Duirk, Gombert et al.

2005) incorporated the reaction of NOM with monochloramine into chloramine

chemistry model to predict chlorine residual loss in the presence of NOM. The authors

proposed a biphasic reaction regime, which is a fast disinfectant demand followed by a

slow long-term loss. It assumes that in the combined region, monochloramine is the

predominant species and free chlorine is produced only through monochloramine

decomposition. Of the total available reactive site in NOM structure, there are fraction S1

which exhibits reactivity to monochloramine and fraction S2 which exhibits reactivity to

98

free chlorine. Subsequently, the concentration of the reactive site DOC1 and DOC2 can

be expressed as the respective fraction of the total TOC. The total of S1 and S2 is ST,

which is the total reactive site fraction in NOM. It can be calculated as DBP formation

potential divided by the initial TOC of the sample. The proposed conceptual reactions are

as follows.

productsDOCHOCl

productsDOCClNHkDOC

kDOC

⎯⎯ →⎯+

⎯⎯ →⎯+2

12

2

1

The primary products of the first reaction are ammonia and chloride, whereas chloride

and oxidized NOM are the potential products of the second reaction (Duirk, Gombert et

al. 2005). The four parameters, S1, S2, kDOC1, and kDOC2, are assumed to be constant for

each NOM source regardless of the experimental condition (Duirk, Gombert et al. 2005).

A variety of NOM sources were used to prepare water samples with deionized water in

the lab. The model was able to predict monochloramine loss under a wide range of

experimental conditions, i.e. pH 6.6 – 9, DOC 1 – 15 mg/L, and initial monochloramine

concentration 0.025 – 0.2 mM (Duirk, Gombert et al. 2005).

In this study, the reaction scheme proposed by Durik et al. (2005) was incorporated into

the Unified Plus Model, and attempt was made to estimate monochloramine loss in a full

scale transmission system.

Massachusetts Water Recourses Authority (MWRA) is one of the large utilities which

have been using chloramination for decades. Its chloramination process had been

optimized and was chosen as the modeled system for this case study. After summer 2005,

the treatment processes of the new 200 MGD treatment plant include ozonation, pH and

alkalinity adjustment, and chloramination. The target operational conditions for

99

chloramination process are pH 9.5-10, carbonate buffer concentration 0.0008 M (40 mg/L

as CaCO3 alkalinity), ionic strength 0.004 M, and (Cl2/N)0 0.9. The MWRA water source

consists of two reservoirs in series, Quabbin Reservoir in the west and Wachusett

Reservoir in the east. Quabbin Reservoir is up gradient with better water quality (e.g.

lower TOC) than Wachusett Reservoir, and its water can be transferred to Wachusett

Reservoir when necessary. Raw water intake is located at the east end of Wachusett

Reservoir.

Weekly average of the full scale data for the following parameters were obtained, raw

water TOC, and UV254 absorbance; post ozonation UV254 absorbance; total chlorine

residual shortly after chloramination process; pH, temperature, TOC, UV254 absorbance,

and total chlorine residual at the end of the clear well; and total chlorine residual at two

other downstream locations in the transmission line.

Total reactive sites for ozonated water was obtained through bottle tests for 14 days

following the procedures described by Duirk (Duirk, Gombert et al. 2005). The

calculated value of ST is 0.112. Tran (Tran 1994) reported the total of total

trihalomethane formation potential (TTHMFP) and total haloacetic acid formation

potential (THAAFP) of the ozonated water to be 0.025. Since TTHM and THAA are only

part of the total DBP, the value is expected to be less than that obtained through the bottle

test. For initial conditions, the pH, temperature, and TOC at the end of the clear well were

used. Although only total chlorine residual is monitored in MWRA system, it is assumed

that monochloramine is the predominant species. The total chlorine residual shortly after

chloramination process was used as the concentration at time zero. The other data points

are available at locations with average detention times of 5 hours, 1.5 days, and 2.5 days.

100

As shown in Figure 6-17, MWRA raw water quality exhibits a seasonal trend in

temperature and UV254 absorbance, which implies the potential variation in the source

of NOM. Other than seasonal lake turn over, the transfer from Quabbin Reservoir also

significantly impacts the water quality at the intake. For calibration purposes, a consistent

NOM source would be desirable. Thus four sets of weekly average data in late June and

early July of 2007 were selected to calibrate the model. The raw water quality was within

the range of 0.079 – 0.09 cm-1 for UV254 absorbance and 13.6 – 15.3°C for temperature.

0.000

0.020

0.040

0.060

0.080

0.100

0.120

8/1/2005

10/30/2005

1/28/2006

4/28/2006

7/27/2006

10/25/2006

1/23/2007

4/23/2007

7/22/2007

10/20/2007

UV2

54, a

bs/c

m

0

2

4

6

8

10

12

14

16

18

20

Tem

pera

ture

, Cel

cius

RawUV254FINB Temp, C

Figure 6-17 Raw water UV254 absorbance and water temperature at the end of the clear well in

MWRA system

Figure 6-18 through 6-21 show the results of model calibration. The four selected

datasets exhibited a consistent trend of the biphasic decay of monochloramine. The

calibrated values for the coefficients are kdoc1= 3.47 M-1s-1, kdoc2= 4.17x104 M-1s-1,

101

S1=0.015, and S2=0.097. Two more datasets from the weekly average full scale data

were selected to validate the model. Figure 6-22 depicts the comparison between model

simulation and the full scale data for the week of July 16th, 2007. Despite the differences

in raw water temperature and NOM from those of the calibration datasets, satisfactory

results were obtained for both fast and slow decay phases. In the other validation using

the full scale data of the week of June 19th 2006, fast decay was under predicted (Figure

6-23), although the raw water temperature and UV254 absorbance were in the similar

range as those of the calibration datasets. These suggest that temperature and raw water

quality are not the only parameters which would impact the fast decay. The operational

conditions of the preceding treatment processes, such as ozone dose and chlorine dose

before ammonia addition, may also impact kdoc1 and S1.

Multiple regression was carried out aiming to explore the potential correlations between

the decrease during the fast decay phase and other parameters, such as raw water

SUVA254 (UV254 absorbance divided by DOC), ozone dose, target chlorine dose, etc.

However, with limited data, no correlation was found to be statistically significant at this

point.

After incorporating the biphasic reaction scheme with NOM (Duirk, Gombert et al. 2005),

the Unified Plus Model successfully predicted the slow decay phase of the

monochloramine decay in the transmission line of the MWRA system. However the fast

decay seems to be impacted not only by raw water characteristics but many other

parameters during full scale operation. No statistically significant correlation was found

yet due to the limited datasets from the full scale system.

102

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3

Time, days

Tota

l chl

orin

e re

sidu

al c

onc.

, mg/

L as

Cl2

Figure 6-18 Comparison between model simulation and full scale data on the week of June 11,

2007 Raw water UV254 0.09 13.6°C

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3Time, days

Tota

l chl

orin

e re

sidu

al c

onc.

, mg/

L as

Cl2


2007 Raw water UV254 0.086 14.7°C

103

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3Time, days

Tota

l chl

orin

e re

sidu

al c

onc.

, mg/

L as

Cl2

Figure 6-20 Comparison between model simulation and full scale data on the week of July 2,

2007 Raw water UV254 0.083 15.3°C

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3

Time, days

Tota

l chl

orin

e re

sidu

al c

onc.

, mg/

L as

Cl2


2007 Raw water UV254 0.079 14.3°C

104

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3Time, days

Tota

l chl

orin

e re

sidu

al c

onc.

, mg/

L as

Cl2


2007 Raw water UV254 0.075 16.1°C

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5 3

Time, days

Tota

l chl

orin

e re

sidu

al c

onc.

, mg/

L as

Cl2


2006 Raw water UV254 0.09 14.3°C

105

7 Conclusions and Recommendations

Conclusions:

1. In light of the newly available data on the rate coefficient of monochloramine

formation reaction, k1 (Qiang and Adams 2004), re-evaluation was carried out on

this specific rate coefficient. Through regression analysis, no correlation was

found between the specific rate coefficient and 1) ionic strength or 2) initial

chlorine to ammonia molar ratio. Incorporating the latest data, the Arrhenius

equation for the specific rate of monochloramine formation reaction was updated

to be

k1=2.04x109exp(-1887/T), which is 3.63x106 M-1s-1 at 25° C.

2. Trichloramine hydrolysis reaction (Kumar, Shinness et al. 1987) was included in

the Unified Plus model. Trichloramine was not determined in this study nor was

any data available from the literature. The result from the sensitivity analysis

showed that at low initial chlorine and ammonia concentration (less than 1x10-4

M), trichloramine hydrolysis reaction seemed not to be significant in either

combined or breakpoint region.

3. Sensitivity analysis showed that in the combined chlorine region, the model was

very sensitive to monochloramine formation and hydrolysis reactions. In the

transition and breakpoint regions, trichloramine formation reaction, Reaction 12,

13, and 14 were more important. Dichloramine formation reaction was shown to

be an important reaction at all conditions tested. Other than trichloramine

106

hydrolysis reaction to which this reaction system did not show any significant

sensitivity, the back reaction of monochloramine disproportionation, i.e. k6, was

not believed to be significant under the reaction conditions studied here (Jafvert

2006).

4. The Unified Plus Model was calibrated and validated to limited data in the

following range, pH 6.5 – 9.5, temperature 4 – 30°C, total carbonate buffer

concentration 9x10-4 – 1x10-2 M, and initial chlorine to ammonia molar ratio 0.5

to 2.0. It can reasonably predict chloramine species concentrations in synthetic

solution using the initial conditions within the above ranges.

5. An open system was found to have significant impact on experiments conducted

using carbonate buffer. Depending on initial pH and total carbonate concentration,

pH could change during the equilibration with atmospheric CO2 and consequently

affect the concentration of chloramine species. Whether the effect of open system

is significant or not in full scale practice dependents on the configuration of the

specific system.

6. With moderate modification, the Unified Plus Model can be used to generate

breakpoint curves, which can demonstrate the effect of open system as well as

degree of mixing on the speciation of chloramine species. This model also was

used to successfully reproduce the observed breakpoint phenomenon during

switching of monochloramine and chlorine.

7. The effect of NOM (Duirk, 2005) was incorporated into the Unified Plus Model

in an attempt to simulate disinfectant loss in full scale system. Limited full scale

data were available for the periods when both temperature and UV254 absorbance

107

of the raw water were within a narrow range. The calibrated model showed

adequate prediction in the selected range of raw water quality, i.e. UV254

absorbance and temperature. Preceding treatment processes may have significant

impact on disinfectant speciation and stability.

Recommendations:

1. The specific rate coefficient of monochloramine formation can be further studied

at high pH, high initial chlorine to ammonia molar ratio, 0.2<(Cl2/N)0<0.8, and

short reaction time, 100 milliseconds, to avoid side reactions such as dichloramine

formation.

2. Although much work had been done trying to identify the unknown intermediate

during dichloramine decomposition (Reaction 7, 8, 9) (Leung and Valentine 1994;

Leung and Valentine 1994), and NOH is used in this study, its chemical form was

never confirmed. More work is needed to identify and quantify it in order to fully

understand the mechanism represented by Reaction 7, 8 and 9.

3. The dichloramine decomposition reactions when free chlorine is present

(Reaction 11 and 12) was postulated by Margerum and adopted by Jafvert and

this work. Further study on the rate coefficients of these general base catalyzed

reactions is necessary to improve the understanding on breakpoint reactions.

4. No experimentally proved reaction mechanism was reported for nitrate formation,

Reaction 14. It is found that when initial chlorine to ammonia molar ratio is larger

than 1, nitrate is produced significantly more at pH 6 -7 than at higher pH. It is

also found that NOM would lead to increase in the production of nitrate and

108

decrease in nitrogen gas when initial chlorine to ammonia molar ratio is less than

1.

5. If more data were available at lower pH (6.6-8) in both combined and breakpoint

regions, where significant dichloramine is present, the Unified Plus Model can be

further calibrated to confirm those rate coefficients for dichloramine

decomposition (Reaction 7, 8, 9, 12, 13, 14).

109

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Hand, V. C. and D. W. Margerum (1983). "Kinetics and Mechanisms of the Decomposition of Dichloramine in Aqueous Solution." Inorg. Chem. 22(10): 1449-1456. Harrington, G. W., D. R. Noguera, et al. (2003). Ammonia From Chloramine Decay: Effects on Distribution System Nitrification, AWWARF. Report No.90949. Huffman, R. P. (1976). The Chemistry of the Inorganic Chloramines and Their Determination in Aqueous Solution. Chemistry Department, Purdue University. Master Thesis. Jafvert, C. T. (1985). A Unified Chlorine-Ammonia Speciation and Fate Model. Civil and Environmental Engineering, University of Iowa. Ph.D Dissertation. Jafvert, C. T. (2006). Personal Communication. Jafvert, C. T. and R. L. Valentine (1987). "Dichloramine Decomposition in the Presense of Excess Ammonia." Wat. Res. 21(8): 967-973. Jafvert, C. T. and R. L. Valentine (1992). "Reaction Scheme for the Chlorination of Ammoniacal Water." Envion. Sci. Technol. 26(3): 577-586. Jain, K. (2007). Effect and Application of Mixing on Chloramination Process. Department of Civil and Environmental Engineering. Boston, MA, Northeastern University. Master Thesis. Johnson, J. D. and J. G. W. Inman (1978). The Kinetics of Chlorine-Ammonia Reactions in Sea Water, Dept. Env Sci & Eng, School of Public Health, UNC; Division of Safeguards, Fuel Cycle and Env Research, Office of Nuclear Regulatory Research, US Nuclear Regulatory Commision. Johson, J. D. and J. G. W. Inman (1978). The Kinetics of Chlorine-Ammonia Reactions in Sea Water, Dept. Env Sci & Eng, School of Public Health, UNC; Division of Safeguards, Fuel Cycle and Env Research, Office of Nuclear Regulatory Research, US Nuclear Regulatory Commision. Kazuyuk, H., I. Yasuhiro, et al. (1998). "Basic Study of CO2 Gas Absorption/Desorption into/from Various Aqueous Solutions." Bullentin of Tsuyama College of Technology(40): 47-53. Kirmeyer, G., K. Martel, et al. (2004). Optimizing Chloramine Treatment 2nd Ed, AwwaRF. Kirmeyer, G., K. Martel, et al. (2004). Optimizing Chloramine Treatment 2nd Ed, AWWARF. Report No. 2760.

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Kumar, K., R. W. Shinness, et al. (1987). "Kinetics and Mechanisms of the Base Decomposition of Nitrogen Trichloride in Aqueous Solution." Inorg. Chem. 26(21): 3430-3434. Leao, S. F. (1981). Kinetics of Combined Chlroine: Reactions of Substitution and Redox School of Engineering. Berkeley, CA, University of California, Berkeley. Ph.D Dissertation. Leung, S. W. and R. Valentine (1994). "An Unidentified Chloramine Decomposition Product - 1. Chemistry adn Characteristics." Water Research 28(6): 1475-1483. Leung, S. W. and R. Valentine (1994). "An Unidentified Chloramine Decomposition Product - II. A Proposed Formation Mechanism." Water Research 28(6): 1485-1495. Lide, D. R. (2005-2006). CRC Handbook of Chemistry and Physics. Boca Raton, Taylor & Francis. Margerum, D. W., E. T. Gray, Jr., et al. (1978). Chlorination and the Formation of N-Chloro Compouds in Water Treatment. Organometals and Organometalloids; Occurence and Fate in the Environment: based on symposium sponsored by the Division of Inorganic Chemistry at the 175th meeting of the American Chemical Society, Anaheim, California, American Chemical Society. McGuire, M. J. (2006). "Eight Revolutions in the History of US Drinking Water Disinfection." Journal AWWA 98(3): 123-149. Morris, J. C. (1966). "The Acid Ionization Constant of HOCl from 5 to 35C." The Journal of Physical Chemistry 70(12): 3798-3805. Morris, J. C. and R. A. Isaac (1980). Interactions of Aqueous Chlorine and Bromine with Nitrogenous Water Contaminants. Cambridge, MA, Division of Applied Sciences, Harvard University. DA MD 17-77-C-7051. Morris, J. C. and R. A. Isaac (1983). A Critical Review of Kinetic and Thermodynamic Constants for the Aqueous Chlorine-Ammonia System. Water Chlorination: Environmental Impact and Health Effects; Volume 4 Book 1:Chemistry and Water Treatment. Ann Arbor, MI, Ann Arbor Science p 49-62. Morris, J. C., I. Weil, et al. (1950). The Formation of Monochloramine and Dichloramine in Water Chlorination. American Chemical Society, Detroit, MI. Palin, A. T. (1950). "A Study of the Chloro Derivatives of Ammonia and Related Compounds, with Special Reference to Their Formation in the Chlorination of Natural and Polluted Waters." Waste Water Eng. 54: 151.

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114

Appendix A Recalculated Values of k1 for Correlation Analysis

115

Table A-1 Recalculated Values of k1 for Correlation Analysis Temp pH μ HOCl0 (Cl2/N)0 NH30 kobs k1 Source

°C M M Molar M M-1s-1 M-1s-1 25 12.05 0.012 7.20E-06 0.5 1.44E-05 1.22E+02 4.45E+06 Weil&Morris1949 25 12.05 0.012 1.44E-05 0.3 4.32E-05 1.22E+02 4.45E+06 Weil&Morris1949 25 12.05 0.012 1.44E-05 0.2 7.20E-05 1.21E+02 4.41E+06 Weil&Morris1949 25 12.05 0.012 2.88E-05 0.4 7.20E-05 1.20E+02 4.38E+06 Weil&Morris1949 25 11.83 0.010 1.13E-05 0.5 2.26E-05 2.33E+02 5.09E+06 Weil&Morris1949 25 11.80 0.030 1.13E-05 0.5 2.26E-05 2.27E+02 4.94E+06 Weil&Morris1949 25 11.78 0.050 1.13E-05 0.5 2.26E-05 2.22E+02 4.84E+06 Weil&Morris1949 25 11.75 0.110 1.13E-05 0.5 2.26E-05 2.18E+02 4.77E+06 Weil&Morris1949 25 11.72 0.210 1.13E-05 0.5 2.26E-05 2.27E+02 4.95E+06 Weil&Morris1949 25 10.95 0.001 1.13E-05 0.5 2.26E-05 1.53E+03 4.20E+06 Weil&Morris1949 25 12.23 0.015 1.13E-05 0.5 2.26E-05 9.67E+01 5.40E+06 Weil&Morris1949 25 12.3 0.021 1.13E-05 0.5 2.26E-05 5.88E+01 3.94E+06 Weil&Morris1949 5.8 11.7 0.012 1.13E-05 0.5 2.26E-05 8.50E+01 8.72E+05 Weil&Morris1949 16.7 11.7 0.012 1.13E-05 0.5 2.26E-05 1.60E+02 2.19E+06 Weil&Morris1949 31 11.7 0.012 1.13E-05 0.5 2.26E-05 3.07E+02 5.57E+06 Weil&Morris1949 35 11.7 0.012 1.13E-05 0.5 2.26E-05 4.70E+02 9.08E+06 Weil&Morris1949 25 - 0.100 1.50E-05 0.02 7.35E-04 - 2.86E+06 Huffman&Margerum1978 25 9.5 0.100 2.00E-03 0.05 3.86E-02 9.53E+03 2.39E+06 Huffman&Margerum197825 9.61 0.100 2.00E-03 0.05 4.34E-02 8.85E+03 2.62E+06 Huffman&Margerum197825 9.66 0.100 2.00E-03 0.04 4.83E-02 7.89E+03 2.54E+06 Huffman&Margerum197825 9.79 0.100 2.00E-03 0.03 7.24E-02 5.91E+03 2.38E+06 Huffman&Margerum197825 9.91 0.100 2.00E-03 0.02 8.69E-02 5.70E+03 2.85E+06 Huffman&Margerum197825 - 0.003 1.60E-04 0.06 2.50E-03 - 2.01E+06 Johnson&Inman1978 25 - 0.031 1.60E-04 0.06 2.50E-03 - 2.84E+06 Johnson&Inman1978 25 - 0.056 1.60E-04 0.06 2.50E-03 - 2.78E+06 Johnson&Inman1978 25 - 0.110 1.60E-04 0.06 2.50E-03 - 3.01E+06 Johnson&Inman1978 25 - 0.210 1.60E-04 0.06 2.50E-03 - 3.00E+06 Johnson&Inman1978 25 - 0.410 1.60E-04 0.06 2.50E-03 - 3.10E+06 Johnson&Inman1978 25 - 0.075 - 0.05 - - 2.97E+06 Qiang&Adam2004

116

25 - 0.075 - 0.07 - - 2.99E+06 Qiang&Adam2004 25 - 0.075 - 0.1 - - 3.07E+06 Qiang&Adam2004 5 - 0.075 - - - - 1.69E+06 Qiang&Adam2004 15 - 0.075 - - - - 2.35E+06 Qiang&Adam2004 35 - 0.075 - - - - 3.68E+06 Qiang&Adam2004 3.9 6.95 0.091 4.36E-04 0.1 4.36E-03 1.44E+03 2.24E+06 Morris&Isaac1980 4 6.95 0.009 4.36E-04 0.1 4.36E-03 2.52E+03 3.22E+06 Morris&Isaac1980

4.5 6.95 0.009 4.36E-04 0.25 1.74E-03 2.71E+03 3.33E+06 Morris&Isaac19804.6 6.95 0.009 4.36E-04 0.25 1.74E-03 2.97E+03 3.62E+06 Morris&Isaac198013.1 6.95 0.009 4.36E-04 0.1 4.36E-03 4.99E+03 3.24E+06 Morris&Isaac198014.5 6.95 0.009 4.36E-04 0.1 4.36E-03 5.85E+03 3.43E+06 Morris&Isaac198020.7 6.95 0.009 4.36E-04 0.1 4.36E-03 9.40E+03 3.58E+06 Morris&Isaac198020.8 6.95 0.009 4.36E-04 0.1 4.36E-03 9.79E+03 3.70E+06 Morris&Isaac198021.2 6.95 0.009 4.36E-04 0.25 1.74E-03 1.48E+04 5.45E+06 Morris&Isaac198021.3 6.95 0.009 4.36E-04 0.25 1.74E-03 1.60E+04 5.87E+06 Morris&Isaac198034 6.95 0.009 4.36E-04 0.1 4.36E-03 2.10E+04 3.36E+06 Morris&Isaac1980

34.1 6.95 0.009 4.36E-04 0.1 4.36E-03 2.34E+04 3.72E+06 Morris&Isaac1980Note: “-” means the listed k1 value is an average over a range of the specific parameter.

117

Appendix B Initial Conditions of Available Data from the Literature

118

Table B-1 Initial Conditions of Available Data from the Literature

Source

Fig No./ Exp No.

T °C

pH

μ M

CTCO3 M

Free Cl2 M

Free NH3 M

Initial Mono

M (Cl2/N)0

Free Cl2 mg/L as

Cl2

Free NH3

mg/L as N

Initial Mono

mg/L as Cl2

Wei, 1972 Exp 4-25 20 7.04 0.0051137 5.00E-03 3.04E-05 1.79E-05 0.00E+00 1.70 2.16 0.25 0.00 Wei, 1972 Exp 4-26 20 7.05 0.0101315 1.00E-02 6.07E-05 3.57E-05 0.00E+00 1.70 4.31 0.50 0.00 Wei, 1972 Exp 4-27 20 7.16 0.0101672 1.00E-02 1.21E-04 7.14E-05 0.00E+00 1.70 8.62 1.00 0.00

Valentine 1998 Fig. 4.1 25 7.64 1.00E-01 4.00E-03 0.00E+00 4.54E-05 1.06E-04 0.70 0.00 0.64 7.53 Valentine 1998 Fig. 4.1 25 7.6 1.00E-01 4.00E-03 0.00E+00 2.19E-05 5.10E-05 0.70 0.00 0.31 3.62 Valentine 1998 Fig. 4.1 25 7.7 1.00E-01 4.00E-03 0.00E+00 1.11E-05 2.60E-05 0.70 0.00 0.16 1.85 Valentine 1998 Fig. 4.1 25 7.7 1.00E-01 4.00E-03 0.00E+00 4.29E-06 1.00E-05 0.70 0.00 0.06 0.71 Valentine 1998 Fig. 4.2 25 7.55 1.00E-01 4.00E-03 0.00E+00 2.19E-05 5.10E-05 0.70 0.00 0.31 3.62 Valentine 1998 Fig. 4.2 25 7.55 5.00E-02 4.00E-03 0.00E+00 2.23E-05 5.20E-05 0.70 0.00 0.31 3.69 Valentine 1998 Fig. 4.2 25 6.55 1.00E-01 4.00E-03 0.00E+00 2.19E-05 5.10E-05 0.70 0.00 0.31 3.62 Valentine 1998 Fig. 4.2 25 6.55 5.00E-02 4.00E-03 0.00E+00 2.23E-05 5.20E-05 0.70 0.00 0.31 3.69 Valentine 1998 Fig. 4.2 25 6.55 5.00E-03 4.00E-03 0.00E+00 2.19E-05 5.10E-05 0.70 0.00 0.31 3.62 Valentine 1998 Fig. 4.4 25 8.3 1.00E-01 4.00E-03 0.00E+00 2.14E-05 5.00E-05 0.70 0.00 0.30 3.55 Valentine 1998 Fig. 4.4 25 6.55 1.00E-01 4.00E-03 0.00E+00 2.14E-05 5.00E-05 0.70 0.00 0.30 3.55 Valentine 1998 Fig. 4.5 25 8.34 1.00E-01 4.00E-03 0.00E+00 3.33E-05 5.00E-05 0.60 0.00 0.47 3.55 Valentine 1998 Fig. 4.5 25 7.56 1.00E-01 4.00E-03 0.00E+00 3.33E-05 5.00E-05 0.60 0.00 0.47 3.55 Valentine 1998 Fig. 4.5 25 6.55 1.00E-01 4.00E-03 0.00E+00 3.33E-05 5.00E-05 0.60 0.00 0.47 3.55 Valentine 1998 Fig. 4.6 25 8.31 1.00E-01 4.00E-03 0.00E+00 5.00E-05 5.00E-05 0.50 0.00 0.70 3.55 Valentine 1998 Fig. 4.6 25 7.55 1.00E-01 4.00E-03 0.00E+00 5.00E-05 5.00E-05 0.50 0.00 0.70 3.55 Valentine 1998 Fig. 4.6 25 6.55 1.00E-01 4.00E-03 0.00E+00 4.80E-05 4.80E-05 0.50 0.00 0.67 3.41 Valentine 1998 Fig. 4.7 4 7.5 1.00E-01 1.00E-02 0.00E+00 2.14E-05 5.00E-05 0.70 0.00 0.30 3.55 Valentine 1998 Fig. 4.7 25 7.5 1.00E-01 1.00E-02 0.00E+00 2.23E-05 5.20E-05 0.70 0.00 0.31 3.69 Valentine 1998 Fig. 4.7 35 7.5 1.00E-01 1.00E-02 0.00E+00 2.14E-05 5.00E-05 0.70 0.00 0.30 3.55 Valentine 1998 Fig. 4.8 25 6.6 1.00E-01 1.00E-02 0.00E+00 2.14E-05 5.00E-05 0.70 0.00 0.30 3.55 Valentine 1998 Fig. 4.9 25 7.6 1.00E-01 1.00E-02 0.00E+00 2.19E-05 5.10E-05 0.70 0.00 0.31 3.62 Valentine 1998 Fig. 4.10 25 8.3 1.00E-01 1.00E-02 0.00E+00 2.14E-05 5.00E-05 0.70 0.00 0.30 3.55

119

Appendix C Experimental Data

120

Table C-1 Experimental Conditions Parameters Exp 1 Exp 2 Exp 3 Exp 4 Exp 5 Exp 6

Temp, C 35 22 4 22 21.5 20 Initial pH 9.52 9.57 9.52 9.54 9.53 9.52

Ionic Strength, M 1.0E-02 1.0E-02 1.0E-02 1.0E-02 1.0E-02 1.0E-02 Buffer CTCO3, M 0.0009 0.0009 0.0009 0.0009 0.0009 0.0009

Initial Free Chlorine, M 5.63E-05 5.63E-05 5.63E-05 5.63E-05 5.63E-05 5.63E-05 Initial Free Ammonia, M 5.95E-05 5.96E-05 5.95E-05 3.31E-05 2.82E-05 4.69E-05

Initial molar (Cl2/N)0 0.95 0.94 0.95 1.70 2.00 1.20 Table C-2 Experimental Results

Exp 1 Time Mono pH s mg/L 0 0.000 1860 4.000 25380 3.950 9.52 105780 3.850 186180 3.725 279900 3.675 456960 3.650 9.50 542520 3.600 626760 3.500 9.49

Exp 2 Time Mono pH s mg/L 0 0.000 3600 3.950 9.49 96600 3.850 183600 3.800 184920 3.800 260400 3.750 336900 3.675 449100 3.650 525180 3.600 610800 3.625 9.45

Exp3 Time Mono pH s mg/L 0 0 21000 4.000 9.39 104400 4.000 195960 3.950 276420 3.900 357240 3.925 450480 3.900 539700 3.850 626880 3.750 9.30

121

Exp 4 Time Free Mono Di pH s mg/L mg/L mg/L 0 4.000 0.000 0.000 9.54 90 1.750 2.225 0.025 9.6 300 1.600 2.380 0.020 600 1.600 2.250 0.000 900 1.575 2.325 0.050 1200 1.550 2.325 0.025 9.2 1500 1.550 2.275 0.025 1800 1.500 2.250 0.050 2100 1.500 2.240 0.020

Exp 5 Time Free Mono Di pH s mg/L mg/L mg/L 0 4 0 0 90 2.200 1.800 0.025 9.55 300 2.150 1.825 0.025 9.55 600 1.900 2.025 0.025 9.61 900 1.850 2.075 0.025 1200 1.800 2.090 0.010 9.55 1500 1.800 2.050 0.000 1800 1.700 2.050 0.050 9.51 2100 1.650 2.000 0.000

Exp 6 Time Free Mono Di pH s mg/L mg/L mg/L 0 4.000 0.000 0.000 120 0.450 3.550 0.000 9.6 300 0.000 4.000 0.000 600 0.450 3.500 0.000 1200 0.400 3.500 0.050 9.55 1500 0.400 3.500 0.050 1800 0.400 3.450 0.050 2100 0.400 3.325 0.050 9.54

122

Appendix D Initial Conditions and Results of Sensitivity Analysis

123

Table D-1 Initial Condition Used for Sensitivity Analysis of the Unified Plus Model Scenarios 1 2 3 4

Temp, C 20 20 20 20 Initial pH 7 9.5 7 9.5 Ionic Strength, M 0.01 0.01 0.01 0.01 Buffer CTCO3, M 0.01 0.01 0.001 0.001 Initial Free Chlorine, M 5.6E-05 5.6E-05 5.6E-05 5.6E-05 Initial Free Ammonia, M 1.1E-04 1.1E-04 1.1E-04 1.1E-04 Initial Monochloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial Dichloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial Trichloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 FIXPH 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial (Cl2/N)0 molar 0.5 0.5 0.5 0.5

Scenarios 5 6 7 8 Temp, C 20 20 20 20 Initial pH 7 9.5 7 9.5 Ionic Strength, M 0.01 0.01 0.01 0.01 Buffer CTCO3, M 0.01 0.01 0.001 0.001 Initial Free Chlorine, M 5.6E-05 5.6E-05 5.6E-05 5.6E-05 Initial Free Ammonia, M 6.3E-05 6.3E-05 6.3E-05 6.3E-05 Initial Monochloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial Dichloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial Trichloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 FIXPH 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial (Cl2/N)0 molar 0.9 0.9 0.9 0.9

124

Table D – 1 (Cont’) Initial Conditions Used for Sensitivity Analysis of the Unified Plus Model Scenarios 9 10 11 12

Temp, C 20 20 20 20 Initial pH 7 9.5 7 9.5 Ionic Strength, M 0.01 0.01 0.01 0.01 Buffer CTCO3, M 0.01 0.01 0.001 0.001 Initial Free Chlorine, M 5.6E-05 5.6E-05 5.6E-05 5.6E-05 Initial Free Ammonia, M 4.7E-05 4.7E-05 4.7E-05 4.7E-05 Initial Monochloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial Dichloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial Trichloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 FIXPH 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial (Cl2/N)0 molar 1.2 1.2 1.2 1.2

Scenarios 13 14 15 16 Temp, C 20 20 20 20 Initial pH 7 9.5 7 9.5 Ionic Strength, M 0.01 0.01 0.01 0.01 Buffer CTCO3, M 0.01 0.01 0.001 0.001 Initial Free Chlorine, M 5.6E-05 5.6E-05 5.6E-05 5.6E-05 Initial Free Ammonia, M 3.3E-05 3.3E-05 3.3E-05 3.3E-05 Initial Monochloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial Dichloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial Trichloramine, M 0.0E+00 0.0E+00 0.0E+00 0.0E+00 FIXPH 0.0E+00 0.0E+00 0.0E+00 0.0E+00 Initial (Cl2/N)0 molar 1.7 1.7 1.7 1.7

125

Table D-2 Calculated Condition Numbers for Monochloramine Scenario 1 Scenario 3 Scenario 5 Scenario 7 k3 -2.44E-02 k3 -2.76E-02 k3 -6.32E-02 k3 -7.03E-02 k2 -1.18E-02 k2 -1.44E-02 k2 -5.52E-02 k2 -6.22E-02 k5H2CO3 -7.89E-03 k5H -1.86E-03 k5H2CO3 -1.27E-02 k10 -5.23E-03 k5HCO3 -3.44E-03 k7 -1.42E-03 k5HCO3 -5.62E-03 k5H -3.02E-03 k7 -1.56E-03 k5H2CO3 -1.01E-03 k10 -4.43E-03 k5H2CO3 -1.65E-03 k5H -1.47E-03 k10 -5.33E-04 k5H -2.42E-03 k5HCO3 -5.47E-04 k10 -5.04E-04 k5HCO3 -3.34E-04 k13 -1.18E-04 k13 -1.02E-04 k13 -1.61E-05 k13 -1.52E-05 k14 -7.39E-05 k14 -7.44E-05 k14 -3.85E-06 k14 -4.18E-06 k11OCL -5.85E-08 k11OCL -1.01E-07 k150 -2.61E-08 k150 -2.93E-08 k150 -3.28E-08 k150 -2.38E-08 k151 -1.41E-08 k151 -1.24E-08 k151 -1.77E-08 k151 -9.85E-09 k15HCO3 -9.32E-10 k15HCO3 -7.80E-11 k15HCO3 -1.17E-09 k15HCO3 -6.16E-11 k152 -1.70E-13 k152 -1.17E-13 k152 -2.10E-13 k152 -8.93E-14 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 1.19E-09 k8&k9 9.17E-10 k11OCL 4.85E-08 k11OCL 5.35E-08 k6 4.05E-07 k6 5.11E-07 k6 3.29E-07 k6 3.39E-07 k11CO3 6.58E-05 k11CO3 5.42E-06 k11CO3 1.33E-05 k11CO3 1.31E-06 k12 1.16E-04 k12 9.89E-05 k12 1.63E-05 k12 1.55E-05 k11OH 4.66E-04 k11OH 3.13E-04 k11OH 1.70E-04 k11OH 1.74E-04 k4 2.24E-03 k7 1.64E-03 k4 3.66E-04 k4 3.74E-04 k7 2.27E-03 k4 2.62E-03 k1 2.45E-02 k1 2.77E-02 k1 6.38E-02 k1 7.13E-02 Scenario 2 Scenario 4 Scenario 6 Scenario 8 k5HCO3 -5.30E-03 k5HCO3 -5.43E-04 k5HCO3 -5.28E-03 k3 -3.47E-03 k3 -3.23E-04 k3 -3.09E-04 k3 -1.89E-03 k2 -2.92E-03 k2 -1.47E-04 k2 -1.41E-04 k2 -1.25E-03 k5HCO3 -1.42E-03 k5H2CO3 -3.97E-05 k5H -5.86E-06 k5H2CO3 -3.95E-05 k5H -1.54E-05 k7 -2.48E-05 k5H2CO3 -3.41E-06 k7 -3.19E-05 k5H2CO3 -8.93E-06 k5H -6.67E-06 k7 -2.58E-06 k5H -6.65E-06 k7 -7.56E-06 k13 -1.38E-07 k13 -1.03E-07 k13 -3.61E-06 k13 -3.10E-06 k14 -1.59E-08 k14 -1.18E-08 k14 -2.40E-07 k14 -2.17E-07 k10 -1.42E-08 k10 -1.29E-09 k10 -1.77E-08 k151 -6.86E-09 k151 -2.02E-10 k151 -1.61E-10 k151 -7.90E-09 k10 -3.78E-09 k15HCO3 -1.41E-11 k15HCO3 -1.10E-12 k15HCO3 -5.50E-10 k15HCO3 -4.68E-11 k150 -1.13E-12 k150 -7.95E-13 k150 -4.44E-11 k150 -3.36E-11 k152 -8.14E-13 k152 -7.39E-13 k152 -3.17E-11 k152 -3.16E-11 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k11OCL 1.18E-12 k11OCL 1.05E-12 k11OCL 3.07E-11 k11OCL 2.62E-11 k6 3.62E-10 k6 4.30E-11 k6 5.19E-11 k6 2.88E-11 k11CO3 1.37E-08 k11CO3 1.15E-09 k11CO3 5.49E-07 k11CO3 5.16E-08 k12 1.37E-07 k12 1.04E-07 k4 1.18E-06 k4 7.11E-07 k11OH 1.58E-07 k4 1.19E-07 k12 3.42E-06 k12 2.92E-06 k4 9.32E-07 k11OH 1.28E-07 k11OH 4.27E-06 k11OH 3.66E-06 k1 3.44E-04 k1 3.31E-04 k1 1.89E-03 k1 3.48E-03

126

Table D – 2 (cont’) Calculated Condition Numbers for Monochloramine Scenario 9 Scenario 11 Scenario 13 Scenario 15 k3 -2.94E-02 k3 -3.20E-02 k3 -6.58E-01 k3 -7.32E-01 k11OH -2.05E-02 k11OH -1.96E-02 k11OH -3.41E-01 k11OH -6.25E-01 k2 -1.33E-02 k2 -1.51E-02 k12 -5.66E-02 k12 -6.83E-02 k7 -3.54E-03 k7 -3.11E-03 k11CO3 -2.17E-02 k7 -7.38E-03 k11CO3 -3.03E-03 k10 -5.41E-04 k7 -5.01E-03 k11CO3 -6.23E-03 k10 -4.89E-04 k11CO3 -2.26E-04 k13 -1.83E-03 k13 -1.29E-03 k5H2CO3 -2.76E-04 k12 -1.34E-04 k11OCL -2.90E-04 k11OCL -4.86E-04 k12 -1.58E-04 k5H -6.97E-05 k2 -2.24E-04 k10 -3.77E-04 k5HCO3 -1.16E-04 k5H2CO3 -3.79E-05 k10 -2.16E-04 k2 -3.70E-04 k5H -4.85E-05 k5HCO3 -1.28E-05 k5H2CO3 -2.07E-05 k5H -4.23E-06 k11OCL -6.91E-06 k11OCL -6.26E-06 k5HCO3 -8.66E-06 k5H2CO3 -2.26E-06 k8&k9 0.00E+00 k8&k9 0.00E+00 k5H -3.65E-06 k5HCO3 -7.15E-07 k152 4.81E-12 k152 2.80E-12 k8&k9 0.00E+00 k8&k9 0.00E+00 k6 1.18E-09 k6 1.62E-09 k6 1.03E-11 k6 1.72E-11 k15HCO3 2.64E-08 k15HCO3 1.81E-09 k152 7.74E-11 k152 8.03E-11 k151 3.99E-07 k151 2.86E-07 k15HCO3 4.28E-07 k15HCO3 5.49E-08 k150 7.37E-07 k150 6.49E-07 k151 6.48E-06 k151 8.81E-06 k13 2.63E-05 k13 1.10E-05 k150 1.21E-05 k150 2.16E-05 k4 4.02E-05 k4 5.17E-05 k4 3.73E-04 k4 7.32E-04 k14 1.28E-03 k14 9.63E-04 k1 2.29E-03 k1 5.05E-03 k1 2.83E-02 k1 3.25E-02 k14 1.07E-01 k14 1.70E-01 Scenario 10 Scenario 12 Scenario 14 Scenario 16 k3 -3.12E-02 k3 -3.02E-02 k3 -7.52E-02 k3 -7.41E-02 k7 -2.75E-03 k7 -2.59E-03 k13 -7.44E-03 k13 -7.01E-03 k13 -2.66E-03 k13 -2.40E-03 k7 -5.00E-03 k7 -5.06E-03 k11OH -7.01E-04 k11OH -3.15E-04 k11OH -4.07E-03 k11OH -3.01E-03 k5HCO3 -1.48E-04 k2 -1.10E-04 k11CO3 -7.76E-04 k11CO3 -7.30E-05 k11CO3 -1.45E-04 k5HCO3 -1.51E-05 k5HCO3 -9.47E-05 k2 -3.57E-05 k2 -1.06E-04 k11CO3 -5.91E-06 k2 -3.45E-05 k5HCO3 -9.63E-06 k10 -2.86E-06 k10 -2.58E-06 k10 -2.47E-06 k10 -2.44E-06 k5H2CO3 -1.07E-06 k5H -1.66E-07 k5H2CO3 -6.87E-07 k11OCL -1.50E-07 k5H -1.79E-07 k5H2CO3 -9.67E-08 k11OCL -1.73E-07 k5H -1.10E-07 k11OCL -7.82E-09 k11OCL -3.84E-09 k5H -1.15E-07 k5H2CO3 -6.46E-08 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k6 1.07E-13 k6 1.03E-13 k6 3.49E-14 k6 3.59E-14 k152 2.72E-09 k152 1.65E-09 k152 3.22E-08 k152 3.06E-08 k150 3.83E-09 k150 1.83E-09 k150 4.58E-08 k150 3.73E-08 k15HCO3 4.73E-08 k15HCO3 2.51E-09 k15HCO3 5.64E-07 k15HCO3 4.90E-08 k151 6.74E-07 k151 3.60E-07 k4 1.71E-06 k4 1.71E-06 k4 1.60E-06 k4 1.53E-06 k151 8.06E-06 k151 7.09E-06 k14 1.68E-04 k14 1.54E-04 k1 1.12E-05 k1 2.09E-05 k1 2.61E-04 k1 2.70E-04 k14 3.22E-04 k14 3.04E-04 k12 2.65E-03 k12 2.39E-03 k12 7.41E-03 k12 6.98E-03

127

Table D-3 Calculated Condition Numbers for Dichloramine Scenario 1 Scenario 3 Scenario 5 Scenario 7 k1 -3.98E-01 k1 -4.97E-01 k7 -1.70E-01 k1 -1.54E-01 k7 -8.90E-02 k7 -8.27E-02 k1 -1.29E-01 k7 -1.48E-01 k10 -2.61E-02 k10 -2.82E-02 k11OH -5.64E-02 k11OH -5.65E-02 k11OH -1.36E-02 k11OH -1.55E-02 k10 -4.18E-02 k10 -4.31E-02 k4 -8.00E-03 k4 -8.71E-03 k4 -1.08E-02 k4 -1.14E-02 k11CO3 -1.06E-03 k12 -3.31E-04 k11CO3 -6.10E-03 k14 -1.05E-03 k12 -3.19E-04 k14 -1.21E-04 k14 -1.03E-03 k11CO3 -5.90E-04 k14 -1.05E-04 k11CO3 -1.16E-04 k12 -4.48E-04 k12 -3.54E-04 k6 -7.20E-06 k6 -7.91E-06 k11OCL -2.57E-06 k11OCL -3.04E-06 k11OCL -3.21E-06 k11OCL -4.10E-06 k6 -2.00E-06 k6 -2.25E-06 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 -5.57E-09 k8&k9 -3.85E-09 k152 1.30E-11 k152 1.02E-11 k152 2.27E-11 k152 1.41E-11 k15HCO3 7.17E-08 k15HCO3 6.80E-09 k15HCO3 1.25E-07 k15HCO3 9.41E-09 k151 1.08E-06 k151 1.08E-06 k151 1.89E-06 k151 1.50E-06 k150 2.01E-06 k150 2.55E-06 k150 3.51E-06 k150 3.53E-06 k13 3.15E-04 k13 3.26E-04 k13 4.59E-04 k13 3.69E-04 k5H 3.15E-02 k5HCO3 7.70E-03 k5H 1.07E-02 k5HCO3 2.19E-03 k5HCO3 7.37E-02 k5H2CO3 2.33E-02 k5HCO3 2.48E-02 k5H2CO3 6.63E-03 k5H2CO3 1.69E-01 k5H 4.27E-02 k5H2CO3 5.57E-02 k5H 1.21E-02 k2 2.32E-01 k2 3.08E-01 k2 1.41E-01 k2 1.60E-01 k3 4.51E-01 k3 5.65E-01 k3 2.14E-01 k3 2.29E-01 Scenario 2 Scenario 4 Scenario 6 Scenario 8 k7 -9.92E-01 k7 -9.93E-01 k7 -9.73E-01 k7 -9.78E-01 k1 -2.25E-02 k1 -1.85E-01 k1 -1.51E-01 k1 -5.63E-01 k10 -5.59E-04 k10 -4.90E-04 k11OH -1.86E-03 k11OH -1.71E-03 k11OH -2.15E-04 k11OH -1.99E-04 k10 -5.56E-04 k10 -4.83E-04 k4 -1.58E-04 k4 -1.39E-04 k4 -1.56E-04 k4 -1.35E-04 k11CO3 -1.62E-05 k14 -2.49E-06 k11CO3 -1.42E-04 k14 -2.46E-05 k12 -4.47E-06 k11CO3 -1.47E-06 k12 -3.88E-05 k11CO3 -1.27E-05 k14 -2.64E-06 k12 -3.59E-07 k14 -2.41E-05 k13 -1.94E-06 k6 -6.15E-08 k6 -5.02E-08 k6 -6.92E-09 k12 -5.06E-07 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k6 -5.48E-09 k11OCL 2.19E-12 k11OCL 1.76E-12 k11OCL 6.71E-11 k8&k9 0.00E+00 k152 9.24E-10 k152 9.35E-10 k152 8.05E-09 k11OCL 8.78E-11 k150 1.29E-09 k150 9.95E-10 k150 1.12E-08 k152 8.20E-09 k15HCO3 1.60E-08 k15HCO3 1.38E-09 k15HCO3 1.39E-07 k150 8.55E-09 k151 2.30E-07 k13 1.54E-07 k151 2.00E-06 k15HCO3 1.20E-08 k13 4.23E-06 k151 2.03E-07 k13 3.62E-05 k151 1.76E-06 k5H 1.15E-03 k5H2CO3 5.00E-03 k5H 9.69E-04 k5H2CO3 1.98E-03 k5H2CO3 6.86E-03 k5H 8.58E-03 k5H2CO3 5.76E-03 k5H 3.40E-03 k3 2.28E-02 k3 1.86E-01 k3 1.57E-01 k5HCO3 3.13E-01 k2 2.30E-02 k2 1.86E-01 k2 1.59E-01 k3 5.75E-01 k5HCO3 8.79E-01 k5HCO3 7.92E-01 k5HCO3 7.39E-01 k2 5.82E-01

128

Table D– 3 (cont’) Calculated Condition Numbers for Dichloramine Scenario 9 Scenario 11 Scenario 13 Scenario 15 k11OH -1.03E-01 k11OH -9.38E-02 k11OH -1.46E+00 k11OH -1.21E+00 k7 -1.98E-02 k1 -1.75E-02 k11CO3 -7.39E-02 k12 -5.13E-02 k11CO3 -1.57E-02 k7 -1.66E-02 k12 -5.15E-02 k11CO3 -1.54E-02 k1 -8.84E-03 k14 -3.71E-03 k7 -1.13E-02 k7 -1.43E-02 k14 -4.31E-03 k10 -2.28E-03 k11OCL -8.37E-04 k11OCL -1.02E-03 k10 -2.17E-03 k11CO3 -1.13E-03 k2 -3.44E-04 k2 -5.74E-04 k4 -4.90E-04 k4 -4.34E-04 k10 -2.35E-04 k10 -3.47E-04 k11OCL -3.22E-05 k11OCL -2.80E-05 k13 -1.10E-04 k4 -1.75E-04 k6 -2.85E-09 k6 -3.58E-09 k4 -5.27E-05 k5H -4.34E-07 k8&k9 0.00E+00 k8&k9 0.00E+00 k5H2CO3 -7.62E-06 k5H2CO3 -2.44E-07 k152 2.44E-11 k152 1.36E-11 k5HCO3 -3.21E-06 k5HCO3 -9.40E-08 k15HCO3 1.34E-07 k15HCO3 8.80E-09 k5H -1.34E-06 k8&k9 0.00E+00 k151 2.03E-06 k151 1.39E-06 k8&k9 0.00E+00 k6 4.03E-12 k150 3.74E-06 k150 3.15E-06 k6 5.59E-12 k152 3.14E-10 k5H 1.29E-04 k5HCO3 2.99E-05 k152 5.66E-10 k15HCO3 2.25E-07 k13 2.72E-04 k5H2CO3 8.82E-05 k15HCO3 3.15E-06 k151 3.66E-05 k5HCO3 3.08E-04 k13 1.57E-04 k151 4.77E-05 k150 9.53E-05 k5H2CO3 7.33E-04 k5H 1.62E-04 k150 8.96E-05 k13 1.15E-04 k12 8.35E-04 k12 6.99E-04 k1 2.96E-03 k1 6.20E-03 k2 1.26E-02 k2 1.72E-02 k14 8.56E-02 k14 1.12E-01 k3 1.52E-01 k3 1.45E-01 k3 1.61E+00 k3 1.19E+00 Scenario 10 Scenario 12 Scenario 14 Scenario 16 k11OH -2.68E-01 k11OH -2.89E-01 k11OH -3.72E-01 k11OH -4.56E-01 k7 -8.38E-02 k7 -8.96E-02 k7 -5.11E-02 k7 -5.42E-02 k12 -3.85E-02 k12 -3.81E-02 k12 -4.00E-02 k12 -4.11E-02 k11CO3 -3.55E-02 k14 -5.60E-03 k11CO3 -3.91E-02 k11CO3 -5.69E-03 k14 -5.37E-03 k11CO3 -4.87E-03 k14 -5.36E-03 k14 -5.63E-03 k10 -7.98E-05 k10 -8.12E-05 k2 -3.10E-05 k2 -2.88E-05 k2 -3.09E-05 k4 -2.64E-05 k10 -2.29E-05 k10 -2.38E-05 k4 -2.54E-05 k11OCL -3.70E-06 k11OCL -1.20E-05 k11OCL -1.19E-05 k11OCL -3.95E-06 k2 -2.72E-06 k4 -9.84E-06 k4 -1.06E-05 k6 -5.82E-13 k6 -6.04E-13 k6 -3.94E-14 k6 -4.55E-14 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k152 1.54E-06 k5H2CO3 1.61E-06 k5H 5.99E-07 k5H2CO3 3.67E-07 k150 2.17E-06 k152 1.72E-06 k152 2.53E-06 k5H 6.22E-07 k5H 2.72E-06 k150 1.94E-06 k5H2CO3 3.57E-06 k152 2.66E-06 k5H2CO3 1.62E-05 k15HCO3 2.64E-06 k150 3.63E-06 k150 3.34E-06 k15HCO3 2.68E-05 k5H 2.74E-06 k1 7.13E-06 k15HCO3 4.33E-06 k1 2.56E-04 k1 2.20E-04 k15HCO3 4.45E-05 k1 2.10E-05 k151 3.87E-04 k5HCO3 2.49E-04 k5HCO3 4.91E-04 k5HCO3 5.39E-05 k5HCO3 2.25E-03 k151 3.87E-04 k151 6.40E-04 k151 6.29E-04 k13 3.84E-02 k13 3.80E-02 k13 3.97E-02 k13 4.08E-02 k3 4.62E-01 k3 4.94E-01 k3 3.26E-01 k3 3.61E-01

129

Table D-4 Calculated Condition Numbers for Free Chlorine Scenario 1 Scenario 3 Scenario 5 Scenario 7 k1 -6.54E-01 k1 -6.07E-01 k1 -3.05E-01 k1 -2.88E-01 k3 -4.25E-02 k3 -4.94E-02 k3 -1.49E-01 k3 -1.74E-01 k5H2CO3 -1.00E-02 k5H -2.57E-03 k5H2CO3 -2.32E-02 k10 -7.48E-03 k5HCO3 -4.48E-03 k5H2CO3 -1.41E-03 k5HCO3 -1.10E-02 k5H -5.89E-03 k5H -1.94E-03 k5HCO3 -4.67E-04 k10 -8.42E-03 k5H2CO3 -3.26E-03 k7 -1.41E-03 k7 -3.25E-04 k5H -4.90E-03 k5HCO3 -1.09E-03 k10 -5.42E-04 k10 -2.27E-04 k14 -7.87E-04 k14 -7.76E-04 k13 -3.99E-05 k13 -3.83E-05 k13 -3.39E-04 k13 -2.88E-04 k14 -2.15E-05 k14 -2.01E-05 k150 -3.60E-07 k150 -4.98E-07 k150 -8.97E-08 k150 -1.24E-07 k151 -1.94E-07 k151 -2.09E-07 k151 -4.84E-08 k151 -5.27E-08 k11OCL -8.65E-08 k11OCL -3.96E-08 k15HCO3 -3.20E-09 k15HCO3 -3.31E-10 k15HCO3 -1.28E-08 k15HCO3 -1.31E-09 k152 -5.80E-13 k152 -4.87E-13 k152 -2.33E-12 k152 -1.96E-12 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 3.78E-09 k8&k9 2.86E-09 k11OCL 7.17E-08 k11OCL 1.11E-07 k6 8.45E-07 k6 1.04E-06 k6 4.37E-07 k6 4.76E-07 k12 3.41E-04 k11CO3 8.93E-05 k12 4.07E-05 k11CO3 6.35E-06 k11CO3 6.64E-04 k12 2.89E-04 k11CO3 5.74E-05 k12 3.95E-05 k11OH 5.68E-03 k11OH 8.00E-03 k11OH 7.23E-04 k11OH 8.28E-04 k4 7.47E-03 k4 8.78E-03 k4 1.39E-03 k4 1.39E-03 k7 2.12E-02 k7 2.44E-02 k2 8.59E-01 k2 8.25E-01 k2 3.61E-01 k2 3.42E-01 Scenario 2 Scenario 4 Scenario 6 Scenario 8 k1 -9.94E-01 k1 -9.94E-01 k1 -9.19E-01 k1 -8.69E-01 k5HCO3 -7.05E-03 k5HCO3 -7.97E-04 k5HCO3 -1.85E-02 k3 -1.43E-02 k3 -6.13E-04 k3 -6.23E-04 k3 -8.48E-03 k5HCO3 -5.62E-03 k5H2CO3 -5.36E-05 k5H -8.62E-06 k5H2CO3 -1.55E-04 k5H -6.26E-05 k7 -2.88E-05 k5H2CO3 -5.02E-06 k7 -5.21E-05 k5H2CO3 -3.64E-05 k5H -9.01E-06 k7 -3.96E-06 k5H -2.61E-05 k7 -1.57E-05 k13 -2.22E-07 k13 -1.52E-07 k13 -1.46E-05 k13 -1.26E-05 k14 -8.75E-08 k14 -4.21E-08 k14 -4.84E-06 k14 -4.27E-06 k10 -1.67E-08 k10 -1.98E-09 k151 -3.17E-08 k151 -2.81E-08 k151 -3.18E-10 k151 -2.38E-10 k10 -2.65E-08 k10 -7.83E-09 k15HCO3 -2.21E-11 k15HCO3 -1.64E-12 k15HCO3 -2.21E-09 k15HCO3 -1.92E-10 k150 -1.78E-12 k150 -1.17E-12 k150 -1.78E-10 k150 -1.38E-10 k152 -1.26E-12 k152 -1.09E-12 k152 -1.27E-10 k152 -1.29E-10 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k11OCL 1.59E-12 k11OCL 1.54E-12 k11OCL 1.21E-10 k11OCL 1.08E-10 k6 4.89E-10 k6 6.33E-11 k6 2.04E-10 k6 1.17E-10 k11CO3 2.17E-08 k11CO3 1.70E-09 k11CO3 2.21E-06 k11CO3 2.12E-07 k12 2.21E-07 k12 1.53E-07 k4 6.08E-06 k4 3.21E-06 k11OH 2.56E-07 k11OH 1.90E-07 k12 1.38E-05 k12 1.19E-05 k4 2.47E-06 k4 3.02E-07 k11OH 1.74E-05 k11OH 1.50E-05 k2 9.98E-01 k2 9.98E-01 k2 9.52E-01 k2 8.96E-01

130

Table D– 4 (cont’) Calculated Condition Numbers for Free Chlorine Scenario 9 Scenario 11 Scenario 13 Scenario 15 k3 -7.28E+00 k3 -7.04E+00 k3 -2.32E-01 k3 -2.32E-01 k1 -6.39E-02 k1 -6.26E-02 k14 -5.18E-02 k14 -6.32E-02 k14 -8.66E-03 k14 -6.69E-03 k13 -2.07E-04 k1 -4.97E-04 k5H2CO3 -3.82E-03 k12 -1.98E-03 k1 -8.10E-05 k13 -1.33E-04 k12 -3.19E-03 k13 -8.06E-04 k150 -5.90E-06 k150 -1.04E-05 k5HCO3 -1.63E-03 k5H -7.69E-04 k151 -3.14E-06 k151 -4.01E-06 k13 -1.11E-03 k10 -6.51E-04 k5H2CO3 -2.09E-06 k5H -3.69E-07 k10 -7.01E-04 k5H2CO3 -4.19E-04 k5HCO3 -8.68E-07 k5H2CO3 -1.96E-07 k5H -6.87E-04 k5HCO3 -1.42E-04 k5H -3.68E-07 k5HCO3 -5.99E-08 k11OCL -6.92E-06 k11OCL -4.81E-06 k15HCO3 -2.07E-07 k15HCO3 -2.47E-08 k150 -2.54E-06 k150 -2.37E-06 k152 -3.73E-11 k152 -3.45E-11 k151 -1.37E-06 k151 -1.03E-06 k8&k9 0.00E+00 k8&k9 0.00E+00 k15HCO3 -9.06E-08 k15HCO3 -6.49E-09 k6 8.77E-13 k6 1.19E-12 k152 -1.65E-11 k152 -9.92E-12 k10 2.27E-06 k10 2.37E-05 k8&k9 0.00E+00 k8&k9 0.00E+00 k4 5.56E-05 k4 9.99E-05 k6 1.53E-08 k6 1.67E-08 k11OCL 6.16E-05 k11OCL 1.19E-04 k4 1.14E-02 k11CO3 1.23E-03 k2 9.55E-05 k2 1.46E-04 k11CO3 1.56E-02 k4 1.20E-02 k7 6.16E-04 k7 1.55E-03 k7 6.79E-02 k7 6.11E-02 k11CO3 4.90E-03 k11CO3 1.76E-03 k11OH 9.58E-02 k11OH 8.63E-02 k12 1.95E-02 k12 2.16E-02 k2 3.36E-01 k2 3.55E-01 k11OH 7.67E-02 k11OH 8.86E-02 Scenario 10 Scenario 12 Scenario 14 Scenario 16 k3 -9.10E-02 k3 -8.74E-02 k3 -5.29E-02 k3 -5.23E-02 k13 -7.76E-03 k13 -6.93E-03 k13 -5.21E-03 k13 -4.94E-03 k7 -7.10E-03 k7 -6.59E-03 k7 -3.21E-03 k7 -3.24E-03 k14 -3.47E-03 k14 -3.20E-03 k14 -2.67E-03 k14 -2.62E-03 k5HCO3 -4.29E-04 k5HCO3 -4.34E-05 k11OH -1.36E-03 k11OH -3.54E-04 k11CO3 -1.42E-04 k10 -6.62E-06 k11CO3 -3.81E-04 k1 -5.51E-05 k10 -7.46E-06 k151 -1.64E-06 k5HCO3 -6.65E-05 k11CO3 -2.85E-05 k5H2CO3 -3.09E-06 k5H -4.76E-07 k1 -6.01E-05 k5HCO3 -6.79E-06 k151 -9.60E-07 k5H2CO3 -2.78E-07 k10 -1.59E-06 k10 -1.57E-06 k5H -5.20E-07 k15HCO3 -1.10E-08 k5H2CO3 -4.83E-07 k5H -7.74E-08 k15HCO3 -6.52E-08 k150 -8.11E-09 k5H -8.10E-08 k11OCL -5.61E-08 k150 -5.27E-09 k152 -7.22E-09 k11OCL -7.00E-08 k5H2CO3 -4.56E-08 k152 -3.73E-09 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k6 2.93E-13 k6 2.46E-14 k6 2.54E-14 k6 3.04E-13 k11OCL 1.61E-08 k152 1.28E-08 k152 1.13E-08 k11OCL 9.34E-09 k4 4.45E-06 k150 1.82E-08 k150 1.37E-08 k4 4.69E-06 k1 9.45E-06 k15HCO3 2.24E-07 k15HCO3 1.80E-08 k1 1.06E-05 k11CO3 1.73E-05 k4 1.21E-06 k4 1.21E-06 k11OH 1.78E-05 k2 4.52E-04 k151 3.20E-06 k151 2.59E-06 k2 4.35E-04 k11OH 1.10E-03 k2 4.37E-05 k2 4.49E-05 k12 7.81E-03 k12 6.98E-03 k12 5.28E-03 k12 4.99E-03

131

Table D-5 Calculated Condition Numbers for Trichloramine Scenario 1 Scenario 3 Scenario 5 Scenario 7 k12 -7.06E-01 k12 -6.99E-01 k12 -8.80E-01 k12 -9.00E-01 k1 -6.81E-01 k1 -6.34E-01 k1 -3.09E-01 k1 -2.94E-01 k13 -3.34E-02 k13 -3.43E-02 k3 -1.41E-01 k3 -1.62E-01 k3 -3.24E-02 k3 -2.69E-02 k5H2CO3 -2.26E-02 k13 -1.12E-02 k7 -1.17E-02 k7 -9.36E-03 k13 -1.35E-02 k10 -7.67E-03 k5H2CO3 -6.38E-03 k10 -1.79E-03 k5HCO3 -1.07E-02 k5H -5.73E-03 k5HCO3 -2.26E-03 k5H -1.04E-03 k10 -9.13E-03 k5H2CO3 -3.17E-03 k10 -1.97E-03 k5H2CO3 -4.63E-04 k5H -4.72E-03 k5HCO3 -1.06E-03 k5H -7.45E-04 k150 -1.18E-04 k14 -8.00E-04 k14 -7.80E-04 k150 -9.00E-05 k5HCO3 -1.17E-04 k150 -3.59E-05 k150 -3.84E-05 k151 -4.86E-05 k151 -5.01E-05 k151 -1.93E-05 k151 -1.61E-05 k14 -2.60E-05 k14 -2.52E-05 k15HCO3 -1.28E-06 k15HCO3 -1.01E-07 k15HCO3 -3.21E-06 k15HCO3 -3.15E-07 k152 -2.32E-10 k152 -1.50E-10 k11OCL -7.26E-09 k152 -4.72E-10 k8&k9 3.68E-09 k8&k9 2.81E-09 k152 -5.83E-10 k8&k9 0.00E+00 k11OCL 1.66E-07 k11OCL 3.13E-07 k8&k9 0.00E+00 k11OCL 1.60E-08 k6 8.09E-07 k6 1.00E-06 k6 9.57E-08 k6 9.41E-08 k4 7.24E-03 k11CO3 6.90E-03 k4 9.82E-04 k4 9.35E-04 k7 1.04E-02 k4 8.59E-03 k11CO3 6.73E-02 k11CO3 6.82E-03 k11CO3 6.82E-02 k7 1.75E-02 k2 8.88E-01 k2 8.55E-01 k2 3.66E-01 k2 3.47E-01 k11OH 9.33E-01 k11OH 9.93E-01 k11OH 9.65E-01 k11OH 1.05E+00 Scenario 2 Scenario 4 Scenario 6 Scenario 8 k1 -1.19E+00 k1 -2.66E+00 k1 -2.12E+00 k1 -5.27E+00 k7 -8.03E-01 k7 -9.68E-01 k13 -7.76E-01 k13 -9.34E-01 k13 -8.02E-01 k13 -9.67E-01 k7 -7.66E-01 k7 -9.23E-01 k12 -2.15E-02 k12 -2.70E-03 k12 -2.46E-02 k12 -6.32E-03 k151 -9.93E-04 k151 -1.01E-03 k151 -9.88E-04 k151 -1.01E-03 k10 -5.44E-04 k10 -4.89E-04 k10 -5.40E-04 k10 -4.79E-04 k4 -1.52E-04 k4 -1.39E-04 k4 -1.47E-04 k4 -1.32E-04 k15HCO3 -6.92E-05 k15HCO3 -6.90E-06 k15HCO3 -6.89E-05 k14 -2.84E-05 k150 -5.58E-06 k150 -4.96E-06 k14 -2.79E-05 k15HCO3 -6.89E-06 k152 -4.00E-06 k152 -4.66E-06 k150 -5.55E-06 k150 -4.91E-06 k14 -2.64E-06 k14 -2.51E-06 k152 -3.98E-06 k152 -4.70E-06 k6 -5.98E-08 k6 -5.01E-08 k6 -6.56E-09 k6 -5.37E-09 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k11OCL 4.78E-10 k11OCL 4.82E-10 k11OCL 4.33E-09 k11OCL 4.37E-09 k5H 1.12E-03 k5H2CO3 4.98E-03 k5H 9.20E-04 k5H2CO3 1.94E-03 k5H2CO3 6.66E-03 k11CO3 7.34E-03 k5H2CO3 5.46E-03 k5H 3.33E-03 k3 2.18E-02 k5H 8.55E-03 k11CO3 7.00E-02 k11CO3 7.32E-03 k11CO3 7.02E-02 k3 1.84E-01 k3 1.32E-01 k5HCO3 2.92E-01 k5HCO3 7.11E-01 k5HCO3 7.75E-01 k5HCO3 5.28E-01 k3 4.99E-01 k11OH 9.28E-01 k11OH 9.91E-01 k11OH 9.15E-01 k11OH 9.77E-01 k2 1.20E+00 k2 2.68E+00 k2 2.24E+00 k2 5.57E+00

132

Table D – 5 (cont’) Calculated Condition Numbers for Trichloramine Scenario 9 Scenario 11 Scenario 13 Scenario 15 k3 -7.27E+00 k3 -7.13E+00 k12 -8.44E-01 k12 -8.09E-01 k12 -1.02E+00 k12 -1.00E+00 k3 -2.30E-01 k3 -2.29E-01 k1 -6.39E-02 k1 -6.29E-02 k14 -5.14E-02 k14 -6.28E-02 k14 -8.68E-03 k14 -6.66E-03 k13 -1.47E-03 k13 -7.81E-04 k13 -4.89E-03 k13 -4.41E-03 k1 -1.04E-04 k1 -5.47E-04 k5H2CO3 -3.81E-03 k5H -7.67E-04 k150 -8.18E-05 k150 -8.88E-05 k5HCO3 -1.63E-03 k10 -5.89E-04 k151 -4.35E-05 k151 -3.31E-05 k10 -6.94E-04 k5H2CO3 -4.18E-04 k15HCO3 -2.87E-06 k5H -4.08E-07 k5H -6.84E-04 k5HCO3 -1.42E-04 k5H2CO3 -2.25E-06 k5H2CO3 -2.17E-07 k150 -1.45E-05 k150 -1.65E-05 k5HCO3 -9.35E-07 k15HCO3 -2.02E-07 k151 -7.86E-06 k151 -7.18E-06 k5H -3.96E-07 k5HCO3 -6.64E-08 k11OCL -4.32E-06 k11OCL -1.48E-06 k152 -5.14E-10 k152 -2.74E-10 k15HCO3 -5.20E-07 k15HCO3 -4.54E-08 k8&k9 0.00E+00 k8&k9 0.00E+00 k152 -9.46E-11 k152 -6.95E-11 k6 9.27E-13 k6 1.29E-12 k8&k9 0.00E+00 k8&k9 0.00E+00 k10 2.78E-06 k10 2.47E-05 k6 1.51E-08 k6 1.65E-08 k4 5.78E-05 k4 1.04E-04 k4 1.14E-02 k11CO3 8.19E-03 k2 1.02E-04 k2 1.56E-04 k7 6.79E-02 k4 1.19E-02 k11OCL 3.97E-04 k11OCL 4.69E-04 k11CO3 9.15E-02 k7 6.17E-02 k7 6.79E-04 k7 1.62E-03 k2 3.37E-01 k2 3.55E-01 k11CO3 7.58E-02 k11CO3 8.55E-03 k11OH 1.73E+00 k11OH 1.77E+00 k11OH 9.70E-01 k11OH 1.06E+00 Scenario 10 Scenario 12 Scenario 14 Scenario 16 k12 -2.33E-01 k12 -2.26E-01 k12 -2.62E-01 k12 -2.64E-01 k13 -1.38E-01 k13 -1.42E-01 k13 -1.28E-01 k13 -1.27E-01 k7 -5.37E-02 k7 -5.84E-02 k7 -2.61E-02 k7 -2.75E-02 k14 -5.75E-03 k14 -5.64E-03 k14 -4.86E-03 k14 -4.84E-03 k151 -3.82E-04 k151 -3.96E-04 k151 -5.38E-04 k151 -5.39E-04 k10 -3.92E-05 k1 -5.98E-05 k1 -6.14E-05 k1 -5.04E-05 k15HCO3 -2.66E-05 k10 -3.99E-05 k15HCO3 -3.75E-05 k10 -9.43E-06 k4 -6.51E-06 k4 -7.96E-06 k10 -9.41E-06 k4 -3.86E-06 k150 -2.15E-06 k15HCO3 -2.71E-06 k4 -3.28E-06 k15HCO3 -3.72E-06 k152 -1.53E-06 k150 -2.00E-06 k150 -3.06E-06 k150 -2.87E-06 k8&k9 0.00E+00 k152 -1.77E-06 k152 -2.14E-06 k152 -2.29E-06 k6 1.45E-14 k6 -3.36E-14 k6 -5.40E-15 k6 -1.14E-14 k5H 6.86E-07 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k1 1.36E-06 k5H2CO3 4.79E-07 k5H 1.97E-07 k5H2CO3 1.33E-07 k11OCL 3.87E-06 k5H 8.18E-07 k5H2CO3 1.17E-06 k5H 2.25E-07 k5H2CO3 4.08E-06 k11OCL 3.77E-06 k11OCL 1.00E-05 k11OCL 1.02E-05 k2 4.69E-04 k5HCO3 7.38E-05 k2 4.54E-05 k5HCO3 1.94E-05 k5HCO3 5.53E-04 k2 5.15E-04 k5HCO3 1.61E-04 k2 5.08E-05 k3 1.09E-02 k11CO3 5.13E-03 k11CO3 4.18E-02 k11CO3 5.05E-03 k11CO3 4.32E-02 k3 2.07E-02 k3 5.84E-02 k3 6.92E-02 k11OH 2.83E-01 k11OH 2.96E-01 k11OH 2.75E-01 k11OH 2.92E-01

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Table D-6 Calculated Condition Numbers for pH Scenario 1 Scenario 3 Scenario 5 Scenario 7 k7 -1.09E-05 k7 -8.59E-05 k7 -4.00E-05 k7 -3.78E-04 k1 -3.64E-06 k1 -6.43E-05 k2 -3.10E-05 k2 -2.15E-04 k10 -3.25E-06 k10 -3.00E-05 k3 -2.26E-05 k10 -1.69E-04 k11OH -1.06E-06 k11OH -1.04E-05 k10 -1.59E-05 k11OH -1.47E-04 k4 -2.37E-07 k4 -2.33E-06 k11OH -1.36E-05 k3 -1.14E-04 k11CO3 -8.26E-08 k14 -1.22E-07 k11CO3 -1.45E-06 k4 -3.13E-06 k14 -1.25E-08 k12 -9.81E-08 k5H2CO3 -1.33E-06 k14 -2.67E-06 k12 -9.45E-09 k11CO3 -7.83E-08 k5HCO3 -5.58E-07 k11CO3 -1.52E-06 k11OCL -2.39E-10 k11OCL -2.66E-09 k14 -2.54E-07 k12 -8.59E-08 k6 -2.14E-10 k6 -2.12E-09 k5H -2.33E-07 k13 -8.30E-08 k8&k9 0.00E+00 k8&k9 0.00E+00 k13 -2.76E-08 k11OCL -9.13E-09 k152 8.97E-16 k152 6.20E-15 k4 -6.58E-09 k6 -6.97E-10 k15HCO3 5.54E-12 k15HCO3 4.56E-12 k11OCL -7.18E-10 k8&k9 -7.34E-13 k151 8.37E-11 k151 7.25E-10 k6 -1.22E-11 k152 3.69E-14 k150 1.55E-10 k150 1.71E-09 k152 5.58E-15 k15HCO3 2.45E-11 k13 6.78E-09 k13 6.94E-08 k8&k9 4.57E-14 k151 3.89E-09 k5H 8.86E-07 k5HCO3 2.01E-06 k15HCO3 3.01E-11 k150 9.18E-09 k5HCO3 2.07E-06 k5H2CO3 6.07E-06 k151 4.55E-10 k5HCO3 1.64E-07 k5H2CO3 4.71E-06 k5H 1.11E-05 k150 8.44E-10 k5H2CO3 5.29E-07 k2 5.27E-06 k2 6.86E-05 k12 1.33E-08 k5H 9.69E-07 k3 7.90E-06 k3 1.10E-04 k1 4.43E-05 k1 3.17E-04 Scenario 2 Scenario 4 Scenario 6 Scenario 8 k5HCO3 -8.59E-06 k5HCO3 -6.06E-06 k5HCO3 -8.63E-06 k3 -4.12E-05 k3 -5.26E-07 k3 -3.47E-06 k3 -3.10E-06 k2 -3.42E-05 k2 -2.31E-07 k2 -1.52E-06 k2 -1.99E-06 k5HCO3 -1.69E-05 k7 -1.39E-07 k7 -9.85E-08 k7 -1.68E-07 k7 -2.65E-07 k5H2CO3 -6.43E-08 k5H -6.54E-08 k5H2CO3 -6.45E-08 k5H -1.82E-07 k5H -1.08E-08 k5H2CO3 -3.81E-08 k5H -1.09E-08 k5H2CO3 -1.06E-07 k13 -2.26E-10 k13 -1.16E-09 k13 -5.96E-09 k13 -3.69E-08 k10 -7.88E-11 k14 -1.77E-10 k14 -5.04E-10 k14 -3.47E-09 k14 -3.32E-11 k10 -4.88E-11 k10 -9.51E-11 k10 -1.31E-10 k151 -3.09E-13 k151 -1.80E-12 k151 -1.28E-11 k151 -8.13E-11 k15HCO3 -2.13E-14 k15HCO3 -1.32E-14 k15HCO3 -8.93E-13 k15HCO3 -5.55E-13 k150 -7.18E-16 k150 -8.71E-15 k150 -7.18E-14 k150 -3.98E-13 k152 0.00E+00 k152 -8.56E-15 k152 -5.14E-14 k152 -3.75E-13 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k8&k9 0.00E+00 k11OCL 2.38E-15 k11OCL 1.15E-14 k11OCL 5.02E-14 k11OCL 3.10E-13 k6 5.88E-13 k6 4.80E-13 k6 8.51E-14 k6 3.42E-13 k11CO3 2.09E-11 k11CO3 1.29E-11 k11CO3 8.90E-10 k11CO3 6.12E-10 k12 2.24E-10 k12 1.17E-09 k4 1.93E-09 k4 8.44E-09 k11OH 2.39E-10 k4 1.33E-09 k12 5.63E-09 k12 3.47E-08 k4 1.51E-09 k11OH 1.44E-09 k11OH 6.83E-09 k11OH 4.32E-08 k1 5.22E-07 k1 2.01E-06 k1 3.03E-06 k1 4.02E-05

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Table D – 6 (cont’) Calculated Condition Numbers for pH Scenario 9 Scenario 11 Scenario 13 Scenario 15 k11OH -9.68E-05 k11OH -8.16E-04 k11OH -1.37E-04 k11OH -1.44E-03 k7 -1.81E-05 k7 -1.43E-04 k12 -1.66E-05 k12 -1.38E-04 k11CO3 -1.47E-05 k10 -2.10E-05 k11CO3 -6.41E-06 k7 -1.63E-05 k2 -2.18E-06 k14 -1.50E-05 k14 -1.33E-06 k11CO3 -1.60E-05 k10 -2.11E-06 k11CO3 -9.96E-06 k7 -1.29E-06 k11OCL -1.11E-06 k14 -1.59E-06 k4 -2.35E-06 k13 -1.99E-07 k13 -6.68E-07 k4 -2.97E-07 k11OCL -2.55E-07 k11OCL -8.08E-08 k10 -4.99E-07 k11OCL -3.10E-08 k6 -1.13E-11 k10 -3.64E-08 k2 -4.25E-07 k6 -9.73E-13 k8&k9 0.00E+00 k2 -1.25E-08 k5H -2.62E-09 k8&k9 0.00E+00 k152 1.21E-13 k5H2CO3 -2.61E-09 k5H2CO3 -1.41E-09 k152 2.33E-14 k15HCO3 7.83E-11 k5HCO3 -1.09E-09 k5HCO3 -4.58E-10 k15HCO3 1.26E-10 k151 1.24E-08 k5H -4.60E-10 k8&k9 0.00E+00 k151 1.91E-09 k150 2.81E-08 k8&k9 0.00E+00 k6 1.21E-14 k150 3.52E-09 k5HCO3 9.98E-08 k6 1.44E-15 k152 3.01E-13 k5H 4.89E-08 k5H2CO3 2.95E-07 k152 4.61E-14 k15HCO3 2.14E-10 k5HCO3 1.17E-07 k5H 5.41E-07 k15HCO3 2.51E-10 k151 3.47E-08 k13 2.26E-07 k13 1.19E-06 k151 3.81E-09 k150 8.94E-08 k5H2CO3 2.78E-07 k2 2.23E-06 k150 7.14E-09 k4 2.68E-07 k12 3.23E-07 k12 2.36E-06 k4 3.27E-08 k1 6.37E-06 k1 2.00E-05 k1 1.46E-04 k1 3.90E-07 k14 3.47E-05 k3 6.50E-05 k3 5.89E-04 k3 6.32E-05 k3 7.31E-04 Scenario 10 Scenario 12 Scenario 14 Scenario 16 k3 -4.67E-05 k3 -3.39E-04 k3 -7.47E-05 k3 -5.80E-04 k7 -4.55E-06 k7 -3.18E-05 k13 -7.39E-06 k13 -5.35E-05 k13 -4.00E-06 k13 -2.66E-05 k7 -5.10E-06 k7 -3.97E-05 k11OH -1.98E-06 k11OH -1.02E-05 k11OH -4.69E-06 k11OH -2.93E-05 k11CO3 -3.41E-07 k14 -1.44E-06 k11CO3 -8.35E-07 k14 -4.28E-06 k5HCO3 -2.20E-07 k2 -7.85E-07 k14 -5.61E-07 k11CO3 -6.32E-07 k14 -2.06E-07 k11CO3 -1.79E-07 k5HCO3 -9.35E-08 k1 -2.12E-07 k2 -9.97E-08 k5HCO3 -1.66E-07 k2 -1.86E-08 k2 -1.53E-07 k10 -4.71E-09 k10 -3.14E-08 k1 -9.87E-09 k5HCO3 -7.30E-08 k5H2CO3 -1.59E-09 k5H -1.82E-09 k10 -2.52E-09 k10 -1.90E-08 k5H -2.67E-10 k5H2CO3 -1.06E-09 k5H2CO3 -6.78E-10 k11OCL -1.30E-09 k11OCL -2.50E-11 k11OCL -1.27E-10 k11OCL -1.92E-10 k5H -8.32E-10 k8&k9 0.00E+00 k8&k9 0.00E+00 k5H -1.14E-10 k5H2CO3 -4.90E-10 k6 0.00E+00 k6 1.01E-15 k8&k9 0.00E+00 k8&k9 0.00E+00 k152 9.34E-12 k152 5.83E-11 k6 0.00E+00 k6 0.00E+00 k150 1.32E-11 k150 6.56E-11 k152 3.64E-11 k152 2.69E-10 k15HCO3 1.63E-10 k15HCO3 8.91E-11 k150 5.19E-11 k150 3.31E-10 k151 2.33E-09 k151 1.30E-08 k15HCO3 6.38E-10 k15HCO3 4.33E-10 k4 2.38E-09 k4 1.68E-08 k4 1.69E-09 k4 1.30E-08 k1 3.33E-07 k1 2.19E-06 k151 9.14E-09 k151 6.27E-08 k12 3.94E-06 k12 2.63E-05 k12 7.23E-06 k12 5.24E-05

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Appendix E Source Code

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'XXXXXXXXXXXXXXXXXXXXXXXXXXXX 'XXXXXXXXXXXXXXXXXXXXXXXXXXXX 'XX Unified Plus Model XX 'XXXXXXXXXXXXXXXXXXXXXXXXXXXX 'XXXXXXXXXXXXXXXXXXXXXXXXXXXX ' ' Cindy Huang ' Civil & Environmental Engineering Department ' Northeastern University ' Boston, Massachusetts ''15 reactions 'With subroutines 'With new reaction coefficients 'July. 29, 2008 ' ' XXXXXXXXXXXXXXX ' XXX options XXX ' XXXXXXXXXXXXXXX 'Option Explicit Option Base 0 ''XXXXXXXXXXXXXXXXXXXXXXXXX ' XXX Reactions modeled XXX ' XXXXXXXXXXXXXXXXXXXXXXXXX 'K1: HOCL+NH3=NH2Cl+H2O 'K2: NH2Cl+H2O=HOCL+NH3 'K3: HOCl+NH2Cl=NHCl2+H2O 'K4: NHCl2+H2O=NH2Cl+HOCl 'K5, KH, KHCO3,KH2CO3: NH2Cl+NH2Cl=NHCl2+NH3 'K6: NHCl2+NH3=NH2Cl+NH2Cl 'K7: NHCl2+H2O=I 'K8: NHCl2+I=HOCl+Products 'K9: NH2Cl+I=Products 'K10: NHCl2+NH2Cl=Products ‘This reaction is excluded for this study. 'K11: KOCL, KOH, KCO3: HOCl+NHCl2=NCl3+H2O 'K12: NHCl2+NCl3+2H2O=2HOCl+Products 'K13: NH2Cl+NCl3+H2O=HOCl+Products 'K14: NHCl2+2HOCL+H2O=NO3- + 5H+ +4Cl- 'K15: NCl3+H2O=HOCl+NHCl2 ' ' XXXXXXXXXXXXXXXXXXXXXXXXX ' XXX declare variables XXX ' XXXXXXXXXXXXXXXXXXXXXXXXX ' 'INPUTS '1.Experiment conditions Dim TEMP As Double

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Dim U As Double ' Ionic Strength Dim TOTAL_CO3 As Double ' carbonate buffer system Dim FIXPH As Double '2.State variables Dim PH As Double Dim FREEN As Double Dim FREECL As Double Dim MONOCL As Double Dim DICL As Double Dim TRICL As Double '3. Differential equations Dim DPH As Double Dim DFREEN As Double Dim DFREECL As Double Dim DMONOCL As Double Dim DDICL As Double Dim DTRICL As Double Dim DN2 As Double Dim DNO3 As Double Dim DCL As Double '4. Ionic strength effect, activity coefficients Dim GAMMA1 As Double Dim GAMMA2 As Double Dim GAMMA3 As Double '5. Reaction coefficients Dim K1 As Double Dim K2 As Double Dim K3 As Double Dim K4 As Double Dim K5 As Double 'K5 is also Dependent variables Dim K5H As Double Dim K5HCO3 As Double Dim K5H2CO3 As Double Dim K6 As Double Dim K7 As Double Dim K8 As Double Dim K9 As Double Dim K10 As Double Dim K11 As Double Dim K11OH As Double Dim K11OCL As Double Dim K11CO3 As Double Dim K12 As Double Dim K13 As Double Dim K14 As Double Dim K15 As Double Dim K150 As Double

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Dim K151 As Double Dim K152 As Double Dim K15HCO3 As Double '6. Equilibrium coefficients and ionization fractions Dim K_HOCL As Double Dim K_NH4 As Double Dim K_H2CO3 As Double Dim K_HCO3 As Double Dim AL_HOCL As Double Dim AL_OCL As Double Dim AL_NH4 As Double Dim AL_NH3 As Double Dim AL_H2CO3 As Double Dim AL_HCO3 As Double Dim AL_CO3 As Double '7. Chlorine to nitrogen molar ratio Dim RATIO As Double '8. Dependent variables Dim HPLUS As Double Dim OH As Double Dim HOCL As Double Dim OCL As Double Dim NH4 As Double Dim NH3 As Double Dim H2CO3 As Double Dim HCO3 As Double Dim CO3 As Double Dim NOH As Double ' Assumed intermediate Dim B As Double ' Buffer Intensity Dim TOTAL_CL As Double 'For mass balancing Dim TOTAL_N As Double 'For mass balancing Dim D As Double ' The denominator in B Dim CL As Double 'chloride for mass balance of the model Dim N2 As Double Dim NO3 As Double 'K5 & K11 are also Dependent variables '9. Run control Dim dt As Double Dim tEnd As Double Dim dtPrint1 As Double Dim dtPrint2 As Double Dim myTime As Double Dim outRow As Integer Dim nextPrintTime As Double

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' XXXXXXXXXXXXXXXXXX ' XXX main model XXX ' XXXXXXXXXXXXXXXXXX ' Sub model() ' ' --- turn autocalc off --- ' Application.Calculation = xlManual ' ' --- get input --- 'Initial condition With Worksheets("Input") TEMP = .Cells(5, 2) PH = .Cells(6, 2) U = .Cells(7, 2) TOTAL_CO3 = .Cells(8, 2) FREECL = .Cells(9, 2) FREEN = .Cells(10, 2) MONOCL = .Cells(11, 2) DICL = .Cells(12, 2) TRICL = .Cells(13, 2) FIXPH = .Cells(14, 2) 'run control dt = .Cells(5, 6) tEnd = .Cells(6, 6) dtPrint1 = .Cells(7, 6) dtPrint2 = .Cells(8, 6) End With ' ' --- preliminary calculations --- ' 'Ionic strength GAMMA1 = 10 ^ (-0.5 * 1 ^ 2 * U ^ 0.5 / (1 + U ^ 0.5)) GAMMA2 = 10 ^ (-0.5 * 2 ^ 2 * U ^ 0.5 / (1 + U ^ 0.5)) GAMMA3 = 10 ^ (-0.5 * 3 ^ 2 * U ^ 0.5 / (1 + U ^ 0.5)) 'Chlorine/Ammonia molar ratio RATIO = (FREECL + MONOCL + 2 * DICL + 3 * TRICL) / (FREEN + MONOCL + DICL + TRICL) 'Equilibrium coefficients

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K_H2CO3 = 10 ^ (-(0.000148 * (TEMP + 273) ^ 2 - 0.0939 * (TEMP + 273) + 21.2)) K_HCO3 = 10 ^ (-(0.000119 * (TEMP + 273) ^ 2 - 0.0799 * (TEMP + 273) + 23.6)) K_HOCL = 10 ^ -(3000 / (TEMP + 273) - 10.0686 + 0.0253 * (TEMP + 273)) K_NH4 = 10 ^ -(0.09018 + 2729.92 / (TEMP + 273)) 'Reaction coefficients K1 = 2.043 * 10 ^ 9 * Exp(-1887 / (TEMP + 273)) 'M-1s-1 CH 2007 K2 = 1.38 * 10 ^ 8 * Exp(-8800 / (TEMP + 273)) 's-1 Morris&Isaac1983 K3 = 300000 * Exp(-2010 / (TEMP + 273)) 'M-1s-1 Morris&Isaac1983 K4 = 2.3 * 10 ^ -3 / 3600 's-1 K5H = 1.05 * 10 ^ 7 * Exp(-2169 / (TEMP + 273)) 'M-2s-1 K5HCO3 = 1035.5 * Exp(-5000 / 1.987 / (TEMP + 273)) ' From calibration K5H2CO3 = 1.438 * 10 ^ 27 * Exp(-36000 / 1.987 / (TEMP + 273)) ' From calibration K6 = 2.67 * 10 ^ 4 'M-2s-1 V K7 = 4 * 10 ^ 5 / 3600 'M-1s-1 V K8 = 10 ^ 8 / 3600 'M-1s-1 V K9 = 3 * 10 ^ 7 / 3600 'M-1s-1 cannot be 0 K10 = 0 K11OCL = 3.24 * 10 ^ 8 / 3600 'M-2s-1 K11OH = 1.18 * 10 ^ 13 / 3600 'M-2s-1 K12 = 1.00 * 10 ^ 14 'M-2s-1 C K13 = 1.00 * 10 ^ 6 'M-2s-1 C K14 = 66 'M-1s-1 C K150 = 1.6 * 10 ^ -6 's-1 K151 = 8 'M-1s-1 K152 = 890 'M-2s-1 K15HCO3 = 65 'M-2s-1 'Zero initial values HPLUS = 0# OH = 0# AL_HOCL = 0# AL_OCL = 0# HOCL = 0# OCL = 0# AL_NH4 = 0# AL_NH3 = 0# NH4 = 0# NH3 = 0#

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AL_H2CO3 = 0# AL_HCO3 = 0# AL_CO3 = 0# H2CO3 = 0# HCO3 = 0# CO3 = 0# B = 0# K5 = 0# NOH = 0# K11 = 0# K15 = 0# CL = 0# NO3 = 0# N2 = 0# ' ' --- main loop --- ' myTime = 0# outRow = 4 nextPrintTime = 0# With Worksheets("Output") ' Clear up output from previous run Call deleteprevious Do While myTime <= tEnd + dtPrint2 'Calculate Initial conditions of dependent variables Call massbalance ' Print output If myTime >= nextPrintTime Then .Cells(outRow, 1) = myTime .Cells(outRow, 2) = PH .Cells(outRow, 3) = FREECL .Cells(outRow, 4) = FREEN .Cells(outRow, 5) = MONOCL .Cells(outRow, 6) = DICL .Cells(outRow, 7) = TRICL .Cells(outRow, 8) = HPLUS .Cells(outRow, 9) = OH .Cells(outRow, 10) = AL_HOCL .Cells(outRow, 11) = AL_OCL .Cells(outRow, 12) = HOCL .Cells(outRow, 13) = OCL .Cells(outRow, 14) = AL_NH4 .Cells(outRow, 15) = AL_NH3

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.Cells(outRow, 16) = NH4 .Cells(outRow, 17) = NH3 .Cells(outRow, 18) = AL_H2CO3 .Cells(outRow, 19) = AL_HCO3 .Cells(outRow, 20) = AL_CO3 .Cells(outRow, 21) = H2CO3 .Cells(outRow, 22) = HCO3 .Cells(outRow, 23) = CO3 .Cells(outRow, 24) = B .Cells(outRow, 25) = K5 .Cells(outRow, 26) = K11 .Cells(outRow, 27) = NOH .Cells(outRow, 28) = TOTAL_CL .Cells(outRow, 29) = TOTAL_N .Cells(outRow, 30) = K15 .Cells(outRow, 31) = GAMMA1 .Cells(outRow, 32) = K_HOCL 'For mass balance .Cells(outRow, 35) = CL .Cells(outRow, 36) = N2 .Cells(outRow, 37) = NO3 .Cells(outRow, 38) = TOTAL_CL + CL .Cells(outRow, 39) = N2 * 2 + NO3 + TOTAL_N outRow = outRow + 1 If myTime < 10 * dtPrint1 Then nextPrintTime = myTime + dtPrint1 Else nextPrintTime = myTime + dtPrint2 End If End If 'Calculate state variables using explicit method Call DiffEquation Call ExplicitSolver myTime = myTime + dt Loop End With ' --- turn autocalc on --- Application.Calculation = xlAutomatic End Sub

143

Sub massbalance() HPLUS = 10 ^ (-PH) OH = 10 ^ (-14) / (HPLUS * GAMMA1) AL_HOCL = HPLUS / (HPLUS + K_HOCL / GAMMA1) AL_OCL = K_HOCL / (HPLUS * GAMMA1 + K_HOCL) HOCL = AL_HOCL * FREECL OCL = AL_OCL * FREECL AL_NH4 = HPLUS / (K_NH4 * GAMMA1 + HPLUS) AL_NH3 = K_NH4 * GAMMA1 / (K_NH4 * GAMMA1 + HPLUS) NH4 = AL_NH4 * FREEN NH3 = AL_NH3 * FREEN AL_H2CO3 = HPLUS ^ 2 / (HPLUS ^ 2 + K_H2CO3 * HPLUS / GAMMA1 + K_H2CO3 * K_HCO3 / GAMMA2) AL_HCO3 = K_H2CO3 * HPLUS / GAMMA1 / (HPLUS ^ 2 + K_H2CO3 * HPLUS / GAMMA1 + K_H2CO3 * K_HCO3 / GAMMA2) AL_CO3 = K_H2CO3 * K_HCO3 / GAMMA2 / (HPLUS ^ 2 + K_H2CO3 * HPLUS / GAMMA1 + K_H2CO3 * K_HCO3 / GAMMA2) H2CO3 = AL_H2CO3 * TOTAL_CO3 HCO3 = AL_HCO3 * TOTAL_CO3 CO3 = AL_CO3 * TOTAL_CO3 If FIXPH < 0.0001 Then B = 2.3 * (HPLUS + OH + AL_NH4 * AL_NH3 * FREEN + (AL_H2CO3 * AL_HCO3 + AL_HCO3 * AL_CO3 + 4 * AL_H2CO3 * AL_CO3) * TOTAL_CO3) Else B = 1000 End If K5 = K5H * HPLUS + K5HCO3 * HCO3 + K5H2CO3 * H2CO3 K11 = K11OH * OH + K11OCL * OCL + K11CO3 * CO3 K15 = K150 + K151 * OH + K152 * OH ^ 2 + K15HCO3 * HCO3 * OH If MONOCL > 0 Then NOH = (K7 * OH * DICL) / (K8 * DICL + K9 * MONOCL) Else NOH = 0 End If TOTAL_CL = FREECL + MONOCL + 2 * DICL + 3 * TRICL

TOTAL_N = FREEN + MONOCL + DICL + TRICL

144

End Sub Sub DiffEquation() DPH = -(K1 * NH3 * HOCL * (AL_NH4 - AL_OCL) _ + K2 * MONOCL * (AL_OCL - AL_NH4) _ + K3 * MONOCL * HOCL * (-AL_OCL) _ + K4 * DICL * AL_OCL _ + K5 * MONOCL ^ 2 * (-AL_NH4) _ + K6 * HPLUS * NH3 * DICL * AL_NH4 _ + 3 * K8 * NOH * DICL _ + K8 * NOH * DICL * AL_OCL _ + 3 * K9 * NOH * MONOCL _ + 3 * K10 * DICL * MONOCL _ + K11 * HOCL * DICL * (-AL_OCL) _ + 3 * K12 * DICL * TRICL * OH _ + 2 * K12 * DICL * TRICL * OH * AL_OCL _ + 3 * K13 * TRICL * MONOCL * OH _ + K13 * TRICL * MONOCL * OH * AL_OCL _ + 5 * K14 * OCL * DICL _ + 2 * K14 * OCL * DICL * (-AL_OCL) _ + K15 * TRICL * AL_OCL _ ) / B DFREEN = -K1 * NH3 * HOCL _ + K2 * MONOCL _ + K5 * MONOCL ^ 2 _ - K6 * HPLUS * NH3 * DICL DFREECL = -K1 * NH3 * HOCL _ + K2 * MONOCL _ - K3 * MONOCL * HOCL _ + K4 * DICL _ + K8 * NOH * DICL _ - K11 * HOCL * DICL _ + 2 * K12 * DICL * TRICL * OH _ + K13 * TRICL * MONOCL * OH _ - 2 * K14 * OCL * DICL _ + K15 * TRICL DMONOCL = K1 * NH3 * HOCL _ - K2 * MONOCL _ - K3 * HOCL * MONOCL _ + K4 * DICL _

145

- 2 * K5 * MONOCL ^ 2 _ + 2 * K6 * HPLUS * NH3 * DICL _ - K10 * DICL * MONOCL _ - K9 * NOH * MONOCL _ - K13 * TRICL * MONOCL * OH DDICL = K3 * MONOCL * HOCL _ - K4 * DICL _ + K5 * MONOCL ^ 2 _ - K6 * HPLUS * NH3 * DICL _ - K10 * DICL * MONOCL _ - K7 * OH * DICL _ - K8 * NOH * DICL _ - K11 * HOCL * DICL _ - K12 * DICL * TRICL * OH _ - K14 * OCL * DICL _ + K15 * TRICL DTRICL = K11 * HOCL * DICL _ - K12 * DICL * TRICL * OH _ - K13 * TRICL * MONOCL * OH _ - K15 * TRICL 'For mass balancing purposes DCL = 2 * K7 * OH * DICL _ + K8 * NOH * DICL _ + K9 * NOH * MONOCL _ + 3 * K10 * MONOCL * DICL _ + 3 * K12 * DICL * TRICL * OH _ + 3 * K13 * TRICL * MONOCL * OH _ + 4 * K14 * OCL * DICL DN2 = K8 * NOH * DICL _ + K9 * NOH * MONOCL _ + K10 * DICL * MONOCL _ + K12 * DICL * TRICL * OH _ + K13 * TRICL * MONOCL * OH DNO3 = K14 * OCL * DICL End Sub

146

Sub ExplicitSolver() PH = PH + DPH * dt FREEN = FREEN + DFREEN * dt FREECL = FREECL + DFREECL * dt MONOCL = MONOCL + DMONOCL * dt DICL = DICL + DDICL * dt TRICL = TRICL + DTRICL * dt CL = CL + DCL * dt N2 = N2 + DN2 * dt NO3 = NO3 + DNO3 * dt End Sub

147

Appendix F Comparison between Model Simulation and Palin’s Data

148

0.0E+00

1.0E-06

2.0E-06

3.0E-06

4.0E-06

5.0E-06

6.0E-06

7.0E-06

8.0E-06

0 18000 36000 54000 72000Time, s

Con

cent

ratio

n, M

NH2Cl NHCl2 Free Cl2DataMono DataDi DataFree

Figure F-1 Comparison between model simulation and data from Palin Exp 6-3

18°C, pH 6.55, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 0.21

0.0E+00

1.0E-06

2.0E-06

3.0E-06

4.0E-06

5.0E-06

6.0E-06

7.0E-06

8.0E-06

0 18000 36000 54000 72000Time, s

Con

cent

ratio

n, M



18°C, pH 7.29, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 0.21

149

0.0E+00

1.0E-06

2.0E-06

3.0E-06

4.0E-06

5.0E-06

6.0E-06

7.0E-06

8.0E-06

9.0E-06

0 18000 36000 54000 72000Time, s

Con

cent

ratio

n, M



18°C, pH 8.62, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 0.21

0.0E+00

1.0E-06

2.0E-06

3.0E-06

4.0E-06

5.0E-06

6.0E-06

7.0E-06

8.0E-06

0 18000 36000 54000 72000Time, s

Con

cent

ratio

n, M



18°C, pH 9.32, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 0.21

150

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-061.0E-05

1.2E-05

1.4E-05

1.6E-05

1.8E-05

2.0E-05

0 18000 36000 54000 72000Time, s

Con

cent

ratio

n, M



18°C, pH 7.05, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 0.51

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-061.0E-05

1.2E-05

1.4E-05

1.6E-05

1.8E-05

2.0E-05

0 18000 36000 54000 72000Time, s

Con

cent

ratio

n, M



18°C, pH 8.52, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 0.51

151

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-061.0E-05

1.2E-05

1.4E-05

1.6E-05

1.8E-05

2.0E-05

0 18000 36000 54000 72000Time, s

Con

cent

ratio

n, M



18°C, pH 9.31, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 0.51

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

3.5E-05

4.0E-05

0 18000 36000 54000 72000Time, s

Con

cent

ratio

n, M



18°C, pH 6.66, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 0.99

152

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

3.5E-05

4.0E-05

0 18000 36000 54000 72000Time, s

Con

cent

ratio

n, M



18°C, pH 7.49, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 0.99

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

3.5E-05

4.0E-05

0 18000 36000 54000 72000Time, s

Con

cent

ratio

n, M



18°C, pH 9.04, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 0.99

153

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 6.91, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.46

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 7.7, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.46

154

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 8.96, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.46

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 9.39, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.46

155

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 6.34, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.58

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 7.53, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.58

156

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 8.26, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.58

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 9.51, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.58

157

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 7.1, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.62

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 7.73, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.62

158

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 8.91, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.62

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 7.17, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.66

159

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 8.06, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.66

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 9.62, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.66

160

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 6.9, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.81

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 8.03, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.81

161

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 8.71, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 1.81

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

8.0E-05

9.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 7.34, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 2.37

162

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

8.0E-05

9.0E-05

0 1800 3600 5400 7200 9000Time, s

Con

cent

ratio

n, M



18°C, pH 9.17, µ 0.001M, CTCO3 0.0015M, (Cl2/N)0 2.37

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