Bromamine Decomposition Revisited: A Holistic Approach for

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Bromamine decomposition revisited: A holistic approach for analyzing acid and base catalysis kinetics David G. Wahman, Gerald E. Speitel, and Lynn E. Katz Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b02661 • Publication Date (Web): 26 Oct 2017 Downloaded from http://pubs.acs.org on October 26, 2017

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Environmental Science & Technology

1

Bromamine decomposition revisited: A holistic approach for analyzing acid

2

and base catalysis kinetics

3

David G. Wahman1*, Gerald E. Speitel Jr.2, and Lynn E. Katz2

4

1

United States Environmental Protection Agency, Office of Research and Development, Cincinnati, OH 45268

5

2

University of Texas at Austin, Department of Civil, Architectural and Environmental Engineering, Austin, TX

6 7 8

9

78712 *

Corresponding author, mailing address: USEPA, 26 W. Martin Luther King Dr., Cincinnati, OH 45268. Phone: (513) 569-7733. Fax: (513) 487-2543. E-mail: [email protected]

TOC/ABSTRACT ART

NH2Br + NH Br 2

NHBr2 + NH3

10 11 12

NHBr2 + H2O N2 + 3Br– + 3H+ + HOBr

Keywords: monobromamine; dibromamine; haloamines; brønsted; catalysis

1

ACS Paragon Plus Environment


13 14

ABSTRACT Chloramine chemistry is complex, with a variety of reactions occurring in series and

15

parallel and many that are acid or base catalyzed, resulting in numerous rate constants. Bromide

16

presence increases system complexity even further with possible bromamine and

17

bromochloramine formation. Therefore, techniques for parameter estimation must address this

18

complexity through thoughtful experimental design and robust data analysis approaches. The

19

current research outlines a rational basis for constrained data fitting using Brønsted theory,

20

application of the microscopic reversibility principle to reversible acid or base catalyzed

21

reactions, and characterization of the relative significance of parallel reactions using fictive

22

product tracking. This holistic approach was used on a comprehensive and well-documented

23

data set for bromamine decomposition, allowing new interpretations of existing data by revealing

24

that a previously published reaction scheme was not robust; it was not able to describe

25

monobromamine or dibromamine decay outside of the conditions for which it was calibrated.

26

The current research’s simplified model (3 reactions, 17 constants) represented the experimental

27

data better than the previously published model (4 reactions, 28 constants). A final model

28

evaluation was conducted based on representative drinking water conditions to determine a

29

minimal model (3 reactions, 8 constants) applicable for drinking water conditions.

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INTRODUCTION

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Free chlorine is a popular distribution system disinfectant choice in the United States

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(US),1-4 but because of Stage 1 and Stage 2 Disinfectants and Disinfection Byproducts Rules

33

implementation, many US utilities now use combinations of chlorine and chloramines to avoid

34

excessive regulated disinfection by-product formation, including trihalomethanes and haloacetic

35

acids.3, 5

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Chloramine chemistry is complex, with a variety of reactions taking place in series and

37

parallel. Some reactions are acid or base catalyzed, which greatly increases the number of rate

38

constants that must be estimated in mechanistic kinetic models of natural waters where carbonate

39

and phosphate are present. When bromide is present in significant concentrations, the system

40

complexity increases even further with possible bromamine and bromochloramine formation

41

under drinking water conditions.6 Therefore, it is impossible practically to generate enough

42

experimental data to estimate rate constants in kinetic models solely using data fitting techniques.

43

Thus, a rational basis for constraining the number of parameters that must be calibrated

44

simultaneously is needed. The current research outlines such a holistic approach using Brønsted

45

theory, application of the microscopic reversibility principle to reversible acid or base catalyzed

46

reactions, and characterization of the relative significance of parallel reactions using fictive

47

product tracking. The approach is demonstrated on a comprehensive and well-documented data

48

set for a relatively simple system examining bromamine decomposition.7, 8

49

The holistic approach allowed new interpretations of existing data, revealing that the

50

reaction scheme employed in previous research was not robust; it was not able to simulate

51

monobromamine (NH2Br) or dibromamine (NHBr2) decay outside of the conditions for which it 3



52

was calibrated (e.g., Figure 1). Thus, a revised reaction scheme for bromamine decomposition

53

was developed that not only reduces the number of estimated parameters but is also robust in its

54

ability to describe data over a significant range of experimental conditions. As the goal of model

55

development is ultimately its practical application, the revised reaction scheme was further

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evaluated to arrive at a minimal model applicable to drinking water practice. The revision of the

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previously published bromamine decomposition reaction scheme and associated new

58

interpretations of existing data is important as the reaction scheme has already been incorporated

59

into models seeking to further extend bromamine chemistry.9

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EXPERIMENTAL SECTION

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Data Set

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No new experimental data were generated. Rather, the data set was taken from stopped-

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flow experiments conducted by Lei, et al.7 and Lei8. A summary of experimental initial

64

conditions is provided in supporting information (SI), Table S2, and the reader is directed to Lei,

65

et al.7 and Lei8 for further data set details.

66

Using absorbance values at 232 nm (A232) and 278 nm (A278) in Appendix A of Lei8,

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NH2Br and NHBr2 concentrations were calculated from molar absorptivity (ε , = 82

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M-1 cm-1; ε , = 425 M-1 cm-1; ε , = 2,000 M-1 cm-1; ε , = 715 M-1

69

cm-1)7 and Eq. 1 and Eq. 2 which are appropriate for a 1 cm absorbance cell path length: NHBr =

A ε , − A ε, (1) ε , ε , − ε , ε,

NH Br =

A − NHBr ε , (2) ε , 4


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Model Reaction rate expressions and stoichiometry The bromamine decomposition model of Lei, et al.7 served as the starting point for the

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current research (Table 1) along with the hypobromous acid (HOBr) and ammonia (NH3)

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reaction to form NH2Br (HOBr + NH3 NH2Br; k = 7.5x107 M-1 s-1).10 The model is composed

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of a general acid-catalyzed NH2Br disproportionation reaction (Table 1, reaction 1), the

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associated general acid-catalyzed reverse of reaction 1 (Table 1, reaction -1), and two general

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base-catalyzed bromamine decomposition reactions (Table 1, reactions 2 and 3). Equilibrium

77

constants of catalytic species were taken from published literature (Table 2) and adjusted to the

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ionic strength used by Lei, et al.7 (0.1 M). Model reactions (Table 1) and required equilibrium

79

equations (Table 2) were implemented into Aquasim.11

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Brønsted Theory

81 82

Brønsted relationship. Individual catalysis constants were related by the Brønsted relationship12 for acid (Eq. 3) and base (Eq. 4) catalysis: k! qK ) log # = log G! + α log # (3) p p k pK ) log # = log G − β log # (4) q q

83

In Eq. 3 and Eq. 4, kA and kB are rate constants for acid and base catalysis, Ka is the respective

84

acid dissociation constant, GA and α and GB and β are constants for a similar series of catalysts

85

where α and β have values between 0 and 1, and p and q are statistical correction factors that

86

represent the number of equally bound dissociable protons (p) and equivalent points where

87

protons can attach (q) and were calculated as outlined by Bell12. When developing the Brønsted

88

relationships, the carbonic acid (H2CO3) true concentration was used rather than the sum of 5



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dissolved carbon dioxide and carbonic acid (H2CO3*), whereas H2CO3* is implemented in the

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Aquasim model.

91

Relative catalyst importance. Because catalysts are typically controlled at relatively

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constant concentrations in experiments (i.e., buffer concentrations and pH), an analysis of

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individual catalyst relative importance to the overall reaction rate constant can be made even for

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complex models with parallel reaction pathways. Such an analysis distinguishes those catalytic

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species that are likely to be important (and therefore likely estimated from the experimental data)

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from those catalytic species that are better estimated from a Brønsted relationship. The

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procedure and an example calculation for determining relative catalyst importance is provided in

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the SI.

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Microscopic Reversibility

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Fast, reversible reactions are common when dealing with haloamine chemistry.

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Application of the microscopic reversibility principle to general acid or base catalysis reactions

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can substantially reduce the required number of estimated parameters (e.g., Table 1, reactions 1

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and -1). Based on the microscopic reversibility principle,13 equilibrium constants are used along

104

with either the forward or reverse reaction rate constants to calculate the other rate constant.

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Equilibrium constant incorporation into the model can be accomplished in at least two ways to

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decrease the required number of parameters. First, published equilibrium constants determined

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experimentally or from thermodynamic estimates can be directly used. For example, referring to

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Table 1, K1 can be used along with k1 to calculate k-1, eliminating the need to estimate the

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individual catalysis constants associated with k-1. Second, published equilibrium constants and

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their associated uncertainty may be used to constrain the allowable range of equilibrium 6


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constants estimated through model fitting to experimental data. The latter method was applied in

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the current research, using the equilibrium constant for reactions 1 and -1 (K1) proposed by

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Trogolo and Arey14 (log K1 = -0.5 ± 1.2, K1 = 0.020-5.0) where the initial guess for K1 was set to

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0.32 and its minimum and maximum allowable values were 0.020 and 5.0, respectively.

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Fictive Products

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Imaginary products, termed fictive products herein, were included in reaction

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stoichiometry (Table 1). Fictive products allowed assessment of reaction pathways during

118

simulations by acting as reaction counters. The magnitude (i.e., concentration) of the fictive

119

product relates to the number of times a particular reaction has occurred in the reaction scheme,

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allowing direct comparisons of parallel reaction pathway importance.

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Fictive product analysis can be employed in at least two circumstances. First, using

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published reaction rate constants, fictive products allow evaluation of which reactions will be

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important under typical conditions (e.g., drinking water conditions). Using fictive products in

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this manner allows selection of the minimal number of reactions required in the kinetic model.

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Second, fictive products can be utilized after a proposed model has been developed to evaluate

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whether all the reactions in the model are indeed required.

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Parameter Estimation

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To estimate parameters in this nonlinear system, an iterative procedure was utilized

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between (i) Aquasim kinetic model parameter estimates from experimental data and (ii) Brønsted

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relationship parameter estimates, which used Aquasim parameter estimates as inputs to estimate

131

additional parameters for subsequent use in the Aquasim kinetic model. Iteration continued until

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the Aquasim parameter estimates converged. 7



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Aquasim. Parameter estimates were obtained in Aquasim using the parameter estimation

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function (secant algorithm) which was configured to minimize residual sum of squares (RSS)

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between measured and model simulated concentrations (Eq. 5): 8

-.. = /012345,6 − 16 7 (5) 69:

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In Eq, 5, ymeas,i is the i-th measurement and yi is the model simulated concentration

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corresponding to the i-th measurement.

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From the 65 experiments (Table S2), 11 were excluded. Six (Br-eff-1, Br-eff-2, Br-eff-3,

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Br-eff-4, Br-eff-5, and Br-eff-6) were excluded (as in Lei, et al.7) because they studied the

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impact of increased bromide, four (HN-1-1, HN-2-1, HN-3-1, and HN-3-2) were excluded

141

because simulated initial NH2Br and NHBr2 concentrations differed substantially from the

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experimental data, and one (CN-1-1) was excluded because it disproportionately contributed to

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the RSS. The remaining 54 experiments were simultaneously fit using absorbance resolved

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NH2Br and NHBr2 concentrations (n = 9,971 data points).

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Brønsted relationship. The Brønsted relationship was used to estimate parameters in

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coordination with the Aquasim kinetic model. Typically, a Brønsted relationship is utilized as a

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post-analysis assessment of estimated parameters and prediction of additional parameters unable

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to be estimated from the experimental data. In the current research, the Brønsted relationship

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was used as an active part of the parameter estimation procedure in an iterative process so that

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the entire set of acid or base catalysts are included in Aquasim parameter estimation, assuring

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self-consistent rate constant estimates are obtained from experimental data and the Brønsted

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relationship.

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Aquasim parameter estimates provided inputs to generate Brønsted relationships.

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Parameters unable to be obtained through Aquasim parameter estimation because of their lack of

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sensitivity in the Aquasim model were resolved from the Brønsted relationship, representing a

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full set of estimated parameters (i.e., Aquasim model and Brønsted relationship estimated

157

parameters). The Brønsted relationship estimated parameters were then entered as fixed

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parameters into the Aquasim model and Aquasim parameter estimation was repeated. The entire

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process iterated until Aquasim model estimated parameters no longer changed.

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RESULTS AND DISCUSSION

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Evaluation of Published Rate Constants

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Upon review of the Lei, et al.7 results (e.g., Figure 1), limitations became apparent. Our

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inability to accurately simulate the breadth of their data using their full model was attributed to

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two factors associated with their data analysis approach. First, Lei, et al.7 made assumptions

165

regarding the importance of the two bromamine decomposition reactions (Table 1, reactions 2

166

and 3). For instance, when they used experiment sets NN-1 and NN-2 to determine ammonia

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catalysis; HN-1, HN-2, and HN-3 to determine hydrogen ion catalysis; and CN-1 and CN-2 to

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determine carbonate buffer catalysis, only reaction 3 for bromamine decomposition was assumed

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important, and reaction 2 was ignored. Importantly, Lei, et al.7 never verified this assumption.

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Second, Lei, et al.7 designated parameter estimates as either “measured” (determined from the

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kinetic model using experimental data) or “predicted” (determined from Brønsted relationships),

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and this terminology is used herein when describing their results. Lei, et al.7 only presented

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simulations using their measured parameters, and no simulations were presented using both their 9



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measured and predicted parameters against their experimental data to evaluate the proposed

175

reaction scheme in its entirety as conducted herein. The impact of these limitations is

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subsequently discussed.

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Reaction importance assumptions. To evaluate the assumption that reaction 2 could be

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ignored for experiment sets NN-1, NN-2, HN-1, HN-2, HN-3, CN-1, and CN-2, a fictive product

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analysis was conducted using both measured and predicted parameters from Lei, et al.7 The

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fictive product analysis allowed a calculation of the percentage of bromamine decomposition

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associated with reaction 2 (Figures S1, S2, and S3). Overall, the analysis showed that between

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53-75% of the bromamine decomposition was attributed to reaction 2 with the balance to

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reaction 3. Therefore, the assumption that reaction 2 could be ignored was not supported by the

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final model. Based on parameters estimated from their analysis, both reactions 2 and 3 were

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required in any data fitting, and reaction 2 was more important for bromamine decomposition

186

than reaction 3. Also, Lei, et al.7 used a step-wise analysis for rate constant estimation (Figure

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S4, Steps 1-4), allowing errors introduced in each estimation step to propagate throughout their

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analysis.

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Validation of full model. Impacts of Lei, et al.7 not performing validation simulations

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using both their measured and predicted rate constants were first accessed by calculating the

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relative importance of catalysts for each reaction. If predicted rate constants are shown to be

192

important, then they should have been included in any simulations conducted. Results for this

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analysis with experiment sets NN-1 and CN-2 are presented in Table 3 (acid-catalysis reactions 1

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and -1) and Table 4 (base-catalysis reactions 2 and 3). For reactions 1 and -1, it appears

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sufficient to only include the measured parameters as they are the only ones that are important to

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the overall reaction rates based on a 5% threshold, except experiments CN-2-3, CN-2-4, and CN10


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2-5 where H2CO3* has minor (5.2-6.6%) importance to the overall rate constant. The same

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cannot be said for reactions 2 and 3. For reaction 2, only the predicted rate constants (OH–,

199

CO32–, and NH3) are important; therefore, final simulations should have been conducted to

200

evaluate the reasonableness of their estimations. For reaction 3, the only predicted rate constant

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that was important was NH3, but it contributes 17-69% to the overall rate constant; therefore, as

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in the case of reaction 2, validation of its estimation from the Brønsted relationship was needed.

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To further assess the implications of Lei, et al.7 not performing simulations including

204

both measured and predicted parameters, simulations using both the measured and predicted rate

205

constants for experiments sets NN-1 (Figure 1) and CN-2 (Figure 2) were conducted. It is

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apparent from these simulations that the implementation of the complete published model for

207

bromamine decomposition provides a poor representation of their experimental data, and because

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of the previously stated concerns regarding their kinetic analysis approach, a reanalysis of the

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experimental data was justified. For reference, a comparison of the current analysis approach

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versus that conducted by Lei, et al.7 is summarized in Figure S4.

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Model evaluation and parameter determination

212

Comparison of various model simulations. An initial attempt was made to include

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both bromamine decomposition reactions (Table 1, reactions 2 and 3) in the reaction scheme as

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proposed by Lei, et al.7, but initial attempts were unsuccessful as the model would not converge

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during simultaneous parameter estimation using the 54 experiments. Therefore, the initial

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conclusion was that the model was overparameterized. To evaluate this initial conclusion, the

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individual experiments of Lei, et al.7 were used to estimate individual rate constants for reactions

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1, -1, 2, and 3. For individual experiments where rate constants for both reactions 2 and 3 could 11



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be estimated (i.e., k2 or k3 not estimated as zero), k2 and k3 were highly, negatively correlated (-

220

0.93 to -1.0), providing evidence of model overparameterization and that both reactions 2 and 3

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were not needed.

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To evaluate the impact of including only reaction 2 or 3, individual parameter estimates

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were conducted for each experiment of Lei, et al.7 using two schemes: (i) Scheme 1 included

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reactions 1, -1, and 2 and (ii) Scheme 2 included reactions 1, -1, and 3. A residual sum of

225

squares (RSS) comparison (Figure S5) showed no apparent advantage for either scheme. Further

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evidence that either reaction scheme would adequately represent the experimental data is

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presented in Figure 3 where simulations are presented for those experiments where selection of

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Scheme 1 over Scheme 2 (Figure 3, Panel A) or selection of Scheme 2 over Scheme 1 (Figure 3,

229

Panel B) provided the greatest RSS reduction. It is evident that even for these worst-case

230

scenarios between schemes, either scheme adequately represented the data. Overall, it was

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concluded that choice of either Scheme 1 or 2 would be adequate and that either, but not both,

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reaction 2 or 3 was required in the reaction scheme as proposed by Lei, et al.7

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Subsequently, three lines of reasoning supported selection of Scheme 1 over 2. First,

234

Cromer, et al.15 studied NHBr2 decomposition and proposed two pathways. The first pathway

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was a tribromamine (NBr3) and NHBr2 reaction which is excluded because Lei, et al.7 found that

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NBr3 was below detection limits. The second proposed pathway was a bimolecular NHBr2

237

reaction consistent with current reaction 2 (Scheme 1). Second, a lower correlation was found

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between estimated parameters for Scheme 1 than 2. Specifically, and for the majority of

239

experiments (Figure S6), k-1 was less correlated with the bromamine decomposition reaction in

240

Scheme 1 (k2, R = -0.31 to 0.57) than Scheme 2 (k3, R = -0.83 to 0.59). Third, based on parallels

12


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with chloramine chemistry, NHBr2 disproportionation (Scheme 1) should occur faster than a

242

reaction of NH2Br and NHBr2 (Scheme 2). Based on these three reasons, Scheme 1 was selected.

243

Model parameter estimation summary. As described previously, an iterative fitting

244

procedure between the Aquasim kinetic model and the Brønsted relationships was used for

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parameter estimation. Through this approach, five acid-catalysis constants for reaction 1 (H2O,

246

HCO3–, NH4+, H2PO4–, and H+), the equilibrium constant for reactions 1 and -1 (K1), and four

247

base-catalysis constants for reaction 2 (OH–, CO32–, HPO42–, and H2O) were estimated in

248

Aquasim. The remaining three acid-catalysis constants for reaction 1 (HPO42–, H2CO3, and

249

H3PO4) and four base-catalysis constants for reaction 2 (PO43–, NH3, HCO3–, and H2PO4–) were

250

estimated from Brønsted relationships. An estimated parameter summary is provided in Table 5

251

(reaction 1) and Table 6 (reaction 2) with corresponding Brønsted plots in Figure 4, showing

252

excellent R2 values of 0.96 and 0.99 for reactions 1 and 2, respectively.

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The relative catalyst importance of the individual constants for each experiment is

254

summarized in Table S3 (reaction 1) and Table S4 (reaction 2). For reactions 1 and 2, all the

255

important constants were directly estimated in Aquasim, except NH3 for reaction 2. Even though

256

the NH3 rate constant for reaction 2 was not estimated in Aquasim, directly including the

257

parameters from the Brønsted relationships ensures consistency between parameters estimated

258

from the experimental data and those estimated from Brønsted relationships.

259

The equilibrium constant estimate for reactions 1 and -1 (K1 = 2.1±0.024) compares

260

favorably to the thermodynamic estimate (log K1 = -0.5 ± 1.2, K1 = 0.020-5.0). Because of the

261

limitations previously stated for the Lei, et al.7 analysis, a direct comparison to the parameters

262

determined in the current research must be done with caution. Regardless, parameters

263

determined for reactions 1 and 2 (Table S5) in this research compare favorably to the previously 13



264

determined parameters from Lei, et al.7, indicating this research offered an improved approach

265

for estimating the kinetic parameters but for the most part did not alter the relative significance

266

of the catalytic species for these two reactions. Importantly however, the current reaction scheme

267

does not include reaction 3 as in the model of Lei, et al.7

268

Simulation summary. Final simulations with the current model and with the measured

269

and predicted parameters from Lei, et al.7 were conducted (Figure S7) and RSS summarized

270

(Figure S8) for each experiment. Based on the total RSS for each experiment (Figure S8, Panel

271

C), the model of Lei, et al.7 marginally reduced the RSS for 9 (PP-1 through PP-5 and HP-1-2

272

through HP 1-5) of the 54 experiments compared to the current model. Whereas, the simplified,

273

current model (3 reactions, 17 constants) represented the experimental data substantially better

274

than that proposed by Lei, et al.7 (4 reactions, 28 constants) in 45 of the 54 experiments as

275

demonstrated by an almost order of magnitude (8 x 10-7 vs. 64 x 10-7) reduction in total RSS for

276

the data set (Figure S8, Panel C). To highlight the improvement with the current model, Figure 5

277

provides simulations and experimental data for experiments selected to investigate the impact of

278

ammonia (NN-1-3 and NN-1-5), carbonate (CN-2-3 and CN-2-5), and phosphate (NP-3 and NP-

279

5) concentrations. Clearly, the current model provides a better experimental data representation

280

along with a reduced RSS. Furthermore, the holistic approach outlined in this research is general

281

in nature and can be applied to kinetic analyses involving acid and base catalysis over a wide

282

variety of conditions.

283

Practical implications

284 285

A final evaluation of the current model was conducted based on representative drinking water conditions to evaluate the minimal model applicable to drinking water. Ten conditions 14


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(Table S6) were selected, including five pHs (6, 7, 8, 9, and 10), a maximum total free ammonia

287

concentration (0.1 mM = 1.4 mg N L-1), a maximum phosphate concentration (0.15 mM = 4.7

288

mg P L-1), and a low (1 mM = 12 mg C L-1) and high (10 mM = 120 mg C L-1) total carbonate

289

concentration. Individual catalyst relative importance to the overall reaction rates is summarized

290

in Table S7 (reaction 1) and Table S8 (reaction 2). Based on excluding species that contribute

291

less than 5% to the overall rate constant of reactions 1 or 2, a model intended for drinking water

292

applications could consist of only a total of eight parameters: (i) four parameters (H2O, HCO3–,

293

H2PO4–, and H+) for reaction 1, (ii) equilibrium constant for reactions 1 and -1, and (iii) three

294

parameters (OH–, CO32–, and H2O) for reaction 2. Validation of the minimal model is an avenue

295

of future research.

296

ASSOCIATED CONTENT

297

Supporting Information Available. Supporting information consists of 53 pages with a

298

section describing the calculation of relative catalyst importance, 8 tables, 8 figures, and

299

associated references. Supporting information is available free of charge at http://pubs.acs.org/.

300

ACKNOWLEDGMENT

301

The USEPA collaborated in the research described herein. It has been subjected to the

302

Agency’s peer and administrative review and has been approved for external publication. Any

303

opinions expressed are those of the authors and do not necessarily reflect the views of the

304

Agency; therefore, no official endorsement should be inferred. Any mention of trade names or

305

commercial products does not constitute endorsement or recommendation for use.

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Lei, H.; Marinas, B. J.; Minear, R. A., Bromamine decomposition kinetics in aqueous solutions. Environ. Sci. Technol. 2004, 38, (7), 2111-2119.

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Table 1. Kinetic model reactions for bromamine decomposition.

a

Current

Lei et al.7

Reaction

Reaction

Number

Number

1

1

2NH Br → NHBr + NH

–1

–1

NHBr + NH @A 2NH Br

2

10

2NHBr + H O → HOBr + N + 3Br B + 3H D

3

9

NH Br + NHBr → N + 3Br B + 3H D

Reaction Stoichiometry

Bromamine Decomposition Revisited: A Holistic Approach for

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