A Comprehensive Kinetic Model for Chlorine Decay and Chlorination Byproduct Formation

John N. McClellan, David A. Reckhow, John E. Tobiason, James K. Edzwald

Department of Civil and Environmental Engineering

University of Massachusetts/Amherst

18 Marston Hall

Amherst, MA 01003

Darrell B. Smith

South Central Connecticut Regional Water Authority

90 Sargent Drive

New Haven, CT 06511

Introduction

Most U.S. water utilities use chlorine to comply with CT requirements, and it is general practice to maintain a low-concentration chlorine residual in water distribution systems. This provides essential public health protection by preventing communication of waterborne infectious disease. Chlorine is a strong oxidant that reacts with the natural organic matter (NOM) present in all natural waters. Although chlorine is invaluable in the protection of public health against waterborne disease, some byproducts of the reactions between chlorine and NOM may represent long-term health risks to water consumers. The trihalomethanes (THMs) and haloacetic acids (HAAs) are two important classes of potentially harmful chlorination byproducts that are currently regulated by the USEPA, and therefore of particular interest to water utilities.

Water suppliers that practice chlorine disinfection face conflicting objectives in providing adequate microbial protection while minimizing the formation of harmful chlorinated organic byproducts. Chlorine/NOM reactions may proceed over a period of days under conditions typical in water distribution systems and variations in the source water quality and in environmental conditions such as temperature and pH can affect the rates and extents of byproduct-forming reactions. As a result of chemical and hydraulic dynamics, the chemical composition of water can vary substantially in time and space in distribution systems. Models that can capture these dynamics would be powerful tools for optimizing water quality in distribution systems.

Mechanistic models are expected to be more robust and flexible than purely empirical models. Mechanistic models may also provide insights into the processes being modeled. It is therefore desirable for kinetic models to reflect the underlying chemistry to the extent possible. Mechanistic modeling has been considered impractical due to the complexity of NOM molecules and NOM/chlorine reaction pathways. However, very complex computations have become feasible using personal computers due to recent advances in computer technology, so that more complex models are practical. The goal of this research is to develop a kinetic model that captures the important mechanistic features of chlorine/NOM reactions.

Background

Existing models. Efforts to model chlorine decay in natural waters began before 1950 (1,2) and a number of studies have been conducted where chlorine decay was modeled in the contexts of drinking water, waste water, and power plant cooling water. The most widely used form for modeling chlorine decay has been the first-order (exponential decay) form. Several investigators have presented empirical models for THM formation as a function of other parameters such as UV absorbance, TOC, pH, temperature and bromide concentration (3-7). These are linear models (in log-transformed variables) that have been fit to large experimental data sets by multivariate linear regression procedures. This approach has also been used to model HAA formation (7). Models that include second-order terms (i.e. terms for both NOM site and chlorine concentration) have been proposed by MacNiell (8), Jedas-Hecart et al. (9), and Clark (10, 11).

Vasconcelos et al. (12) compared several models by fitting them to data sets from bottle tests of eleven different treated waters. Goodness of fit (as measured by the adjusted coefficient of determination R2) for the widely used first-order model was generally poor. For other models compared by Vasconcelos et al. (12), reasonably good fits were achieved with wide variations in the parameter values for the various data sets. This lack of robustness of model parameters is a shortcoming of existing models that we hope to improve with a more mechanistic modeling approach. A mechanistic approach where reactant concentrations and important environmental variables are represented explicitly should be well suited for practical applications such "what if" modeling, modeling of "reactive" chlorination byproducts, and modeling distribution systems with multiple sources of different NOM quality or different chlorine doses.

Reaction mechanisms. The aqueous chlorination of organic compounds has been studied by a number of researchers (13-22). The organic substrates investigated included various pure ketones, organic acids, and aromatics as well as organic fractions extracted from natural waters. Some key findings that bear on the development of a mechanistic model are summarized in this section.

Under conditions typical in water treatment, HOCl and OCl- predominate and Cl2 is not present in significant concentrations. HOCl is expected to be more reactive as an oxidant and halogenating agent than OCl- (23). The functional groups within NOM molecules that have been implicated as important chlorine consumers and byproduct precursors include activated aromatics (particularly those with meta hydroxyl substituents) and some oxygen-rich ketones and keto-acids (16-21). For several ketones and keto-acids, the rate of reaction with halogens is first-order in ketone and not sensitive to halogen concentration except at very low levels (13-15). The reason is a rate-limiting initial dissociation of a proton to form enolate, the reactive species. In the classic haloform reaction of halogens with methyl ketones, enolate formation is followed by a faster halogen addition. After the initial halogenation the remaining protons are more acidic so that the second and third ionizations and halogenations proceed rapidly followed by base-catalyzed hydrolysis to form haloform (23).

For orcinol and resorcinol, the O-substituted species react much faster with chlorine than the corresponding OH substituted species. Nevertheless, the completely protonated species are predominant and are expected to be the most significant participants in chlorine reactions over the pH range of interest in water treatment (22). Acid-base chemistry would play a more important role for aromatics with more acidic substituents, and a first-order rate-limiting step similar to the rate-limiting step of the haloform reaction could be envisioned.

Most of the reaction mechanisms that have been proposed for chloroform formation pass through a trichloromethyl ketone intermediate (16, 19, 21). Chlorine concentration and pH can affect the speciation of products even where reactions of the intermediate are not rate-limiting steps in the overall reaction (21, 24).

The objective is to capture the most important elements of the reaction, i.e. the elements that control the overall reaction rate, and those that affect the proportions of products that are formed. Based on the reaction mechanisms that have been proposed, it seems appropriate to include two conceptual reaction pathways in the model: one with second-order kinetics, and one with a rate-limiting first-order step similar to the haloform reaction. Chlorine consumption and byproduct formation rates will be determined as functions of the reaction rates through these conceptual pathways.

Experimental

A series of bench-scale experiments was conducted to characterize the effects of temperature, pH, and reactant concentrations on chlorine decay and byproduct formation in a treated water. These experiments were conducted using three samples collected at different times from the same source, filter effluent of the Lake Gaillard Water Treatment Plant, No. Branford, CT. This plant treats an impounded surface water source. The process includes alum coagulation, flocculation, and anthracite/sand filtration. Table 1 gives UV absorbance and TOC values for each of the samples.

Table 1. TOC and UV Absorbance of samples used for bench scale experiments.

Date Sample Collected

UV Abs., 254 nm

(cm-1)

TOC

(mg/L)

7/1/97

0.030

1.91

11/14/97

0.028

2.11

7/21/98

0.029

1.97

A series of bottle tests was conducted with each sample. For these tests, four-liter batches were prepared by adjusting pH and temperature to the desired values (and diluting with deionized water in some cases). Batches were then chlorinated and dispensed into 300 mL bottles. Table 2 shows the conditions used for the bench scale experiments.

Table 2. Bench scale bottle test experiments.

Date

Sample

Collected

 

Set

 

N1

Cl2

Dose

(mg/L)

Temp.

(° C.)

 

pH

 

[NOM]2

7/1/97

2

10

4.0

15

7.3

1

 

3

10

1.3

15

7.3

1

 

4

10

2.5

15

6.3

1

 

5

10

2.5

15

7.3

1

 

6

10

2.5

15

8.5

1

 

7

10

2.5

20

7.3

1

 

8

10

2.5

10

7.3

1

 

9

10

2.5

2

7.3

1

 

10

10

2.5

15

7.3

0.67

11/14/97

1

10

2.7

15

7.3

1

 

2

10

1.3

15

7.3

1

 

3

10

2.7

15

7.3

0.5

 

4

10

2.7

25

7.3

1

 

5

10

2.7

2

7.3

1

 

6

10

2.7

15

6.3

1

 

7

10

2.7

15

8.5

1

7/21/98

1

10

2.5

15

7.3

1

 

4

6

2.5

2

9.0

1

 

5

6

2.5

20

9.0

1

 

6

6

2.5

2

6.0

1

 

7

6

2.5

20

6.0

1

1 number of individual observations

2 fraction of undiluted concentration (varied by dilution with deionized water)

Bottles were stored headspace-free in the dark at the desired temperature and removed at intervals for measurement of free chlorine, THMs, and HAAs. Chlorine measurements were made using the DPD Titrimetric Method (25). Trihalomethanes and haloacetic acids were measured using methods similar to EPA Methods 551.1 and 552.2, respectively. Each "set" corresponds to a 4 L batch chlorinated under a specific set of conditions, with 7 to 10 measurements (N) made at intervals ranging from 1 minute to 7 days.

 

Model Description

Three classes of reactive functional groups within the NOM are hypothesized. These are: 1) Sites that react with chlorine instantly relative to the time scale of interest (minutes to days). These reactions are treated as constants (e.g. "instantaneous chlorine demand") in the model. 2) Sites that react with chlorine (HOCl or OCl-) where the first (rate-limiting) step is second-order (first-order in NOM and first-order in chlorine). These are called S1 sites. 3) S2 sites, where there is a rate-limiting initial step that is first-order in NOM, leading to an active form (S2-) that participates in a faster second-order reaction with HOCl. The prototype for the S2 reaction pathway is the classical haloform reaction of ketones with halogens, where the rate-limiting step (first-order in ketone) is a proton dissociation to form enolate. For the S1 and S2 pathways, a series of faster chlorine-consuming steps follow, producing halogenated and oxidized organic compounds, CO2, and Cl-. The amount of formation of each byproduct is an initial amount (representing "instantaneous" formation) plus the sum of specified fractions of the total site consumption through the S1 and S2 pathways. The rate of chlorine consumption is equal to the total rate of site consumption through each pathway multiplied by stoichiometric coefficients representing consumption in intermediate fast steps. The conceptual reaction mechanism is depicted in schematic form in Figure 1.

Equation (1.1) represents the S1 pathway reaction rate, and equations (1.2), (1.3), and (1.4) represent rates related to the S2 pathway.

(1.1)

(1.2)

(1.3)

(1.4)

 

The terms R1, R21f, R21r and R22 are rates, k'1, k'21f, k'21r, and k'22 are apparent rate constants, and [S1], [S2H], and [S2-] represent NOM site concentrations.

Figure 1. Conceptual Reaction Mechanism

Equations (2) represent the rates of consumption of the reactants (chlorine and NOM sites),

(2.1)

(2.2)

(2.3)

(2.4)

 

where n1 and n2 are stoichiometric coefficients that account for chlorine consumption in intermediate steps and the other terms are as described above for equations (1). We have found that the formation kinetics of di- and tri- halogenated HAA species are quite different, so we have treated them as separate groups, with "DHAA" representing the sum of di-halogenated HAA species, and "THAA" representing the sum of tri-halogenated HAA species (Our experiments were conducted using a low-bromide water, so that DHAA= DCAA+BCAA, and THAA=TCAA). We denote total trihalomethane as "TTHM." Equations (3) describe the rates of formation of TTHM, THAA, and DHAA.

(3.1)

(3.2)

(3.3)

 

The a factors represent the fraction of site consumption through each pathway that results in formation of the respective products.

Equations (1), (2) and (3) comprise the basic framework of the model. The equation system must be integrated using numerical methods. For a particular water and set of environmental conditions, a set of apparent rate constants k', factors n and a, and initial site concentrations [S1], [S2H], and [S2-] can be determined by fitting to experimental data. However, for a particular water, the apparent rate constants and factors may vary with environmental conditions. An important objective is to capture these effects in the model. To achieve this objective, we incorporated a mechanistic treatment of the effects of temperature and pH. Equation (4.1) relates the apparent rate constant k1 to fundamental rate constants, including temperature and pH effects. Here, k11 and k12 are the rate constants for the reaction of S1 sites with HOCl and OCl- respectively, and aHOCl and aOCl- are pH-dependent distribution factors for the chlorine species. The term q1 with reaction temperature T and reference temperature Tref is the standard engineering representation of the Arrhenius expression.

(4.1)

 

Equations (4.2), (4.3), and (4.4) describe the apparent rate constants k21f, k21r, and k22. The rates R21f and R21r represent the forward and reverse components of an acid-base equilibrium reaction, with the forward rate treated as an uncatalyzed reaction with water and the reverse rate dependent on proton concentration.

 

(4.2)

(4.3)

(4.4)

 

Equations (5) and (6) describe the distribution factors that relate the relative proportions of products to temperature and pH. Our experimental work suggests that substantial THM and THAA formation occurs through competitive pathways. We hypothesize a common pathway leading to a penultimate intermediate that may form either THM by hydrolysis, or THAA by oxidation (21). In our model, the following distribution factors account for the effects of temperature and pH on this hydrolysis/oxidation competition (equations 5):

(5.1)

(5.2)

 

where kp represents uncatalyzed hydrolysis, kP,OH represents base-catalyzed hydrolysis, kP,HOCl represents oxidation, a1,P is the fraction following the hydrolysis pathway, and a2,P is the fraction that follows the oxidation pathway. The distribution factors for the individual byproduct species are linear combinations of the factors given in equations (5). The general form of the distribution factors for individual species is given in equations (6), where the generic subscript DBP denotes TTHM, DHAA, or THAA.

(6.1)

(6.2)

 

In practice, not all of the right hand side terms are included for an individual species: b1 and b2 are included in the DHAA terms, b1, b11, and b21 are included in the THAA terms, and b12, and b22 are included in the TTHM terms.

 

Calibration and Computation

As stated above, the form of the proposed model is a set of differential equations with known initial conditions that must be solved numerically. Calibration and computational issues are discussed in this section. Two software packages were used for computations and data analysis in this work: the Scientist® data fitting package (26) and a program written by the authors.

Calibration. In order for numerical optimization routines to converge on a solution with the proposed model, initial parameter estimates that are very close to their optimum values are required. We utilized Windows-based computer graphics to make initial parameter estimates. A program was developed that allows adjustment of the model parameters with slide bars while displaying experimental data with the model predictions superimposed. These initial estimates were utilized with the Scientist® (26) software package to find values that resulted in minimum sums of squared residuals. For purposes of model fitting, all response variables were normalized with respect to their average values in the calibration data set. The parameters were optimized with respect to all response variables simultaneously with no weighting. Model parameters and estimated values are presented in Table 3.

Table 3. Model Parameters.

Parameter

Units

Fitted Value

S1 Path

k11

mM-1 hr-1

0.0347

k12

mM-1 hr-1

9.70 x 10-4

q 1T-20° C

T in ° C

1.0996

S2 Path

k21f 1

hr-1

7.18 x 10-3

k21r

mM-1 hr-1

1.44 x 107

k22

mM-1 hr-1

0.854

q 21

q T-20: T in ° C

1.089

Cl2 Demand

n12

Dimensionless

8

n22

Dimensionless

4

Byproduct Formation

kP2

Dimensionless

1

kP,HOCl

mM-1

0.0620

kP,OH

M-1

9.82x106

q P

q T-20: T in ° C

1.007

b12,THM

Dimensionless

0.201

b 22,THM

Dimensionless

0.0956

b 1,TCAA

Dimensionless

0.0387

b 11,TCAA

Dimensionless

0.0272

b 21,TCAA

Dimensionless

0.0777

b 1,DCAA

Dimensionless

0.0346

b 2,DCAA

Dimensionless

0.0345

1Rate assumed to be diffusion-limited. Not treated as adjustable parameter, approximate value from reference (27)

2Fixed arbitrarily, not treated as adjustable parameter.

There are two types of parameters in the model: rate constants, and parameters that represent initial NOM site concentrations that cannot be measured and therefore must be determined by fitting the model to experimental data. There are a total of 19 parameters listed in Table 5. Of these, 15 are adjustable, with values estimated by fitting to bench scale data. Rate R21r is assumed to be diffusion limited, and constant k21r is therefore estimated based on a literature value (27). The intermediate step chlorine consumption coefficients n1 and n2 cannot be determined independently from the other rate constants and have been set arbitrarily. The values for n1 and n2 are rough estimates of the chlorine consumed in forming chloroform from dihydroxybenzene and methyl ketone respectively. The byproduct formation parameter kP is not independent of the paramters kPOH and kPHOCL and is therefore set arbitrarily to unity.

Numerical schemes. The Scientist® package includes several numerical routines including an explicit (Euler) scheme, a fourth-order Runge-Kutta scheme, and a scheme designed for stiff equations called the EPISODE scheme (26). We found that the EPISODE scheme produced the best combination of accuracy and computational speed. The scheme used in the in-house program is a second-order mid-point scheme with a time step of 0.1 hours. Under this scheme, explicit response variable estimates at the time-step mid points are used to advance the solution.

Model Comparison

Calibration data set comparison. The proposed model was compared with two other model forms: the power function form described by Amy et al. (6), and the second order form presented by Clark (10, 11). This comparison was intended to evaluate the capacity of the model form to capture the effects of changes in pH, temperature, initial chlorine concentration, and NOM concentration for a specific water. This comparison does not reflect the generality of the models. Each model was calibrated using our bench scale data set. The power function model was calibrated by multiple linear regression using log-transformed variables. The proposed mechanistic model and the second-order model were calibrated using a numerical least-squares minimization routine (26). Results of the comparison are presented in Table 4. Table 4 shows that the mechanistic model gives a superior fit to the data set compared to either the power function or second-order forms, as measured by the adjusted coefficient of multiple determination R2adj, although all three models fit the data well.

Table 4. Comparison of models: calibration data set.

 

Model Form

Parameter

Mechanistic

Power Function

Second-Order

Number of adjustable parameters

21

28

25

Number of data points

770

770

770

Sum of squared observations

973

973

973

Sum of squared deviations

14.3

21.9

28.6

R2adj

0.985

0.971

0.970

 

 

Outside Data Set Comparison. The model was fit to a data set from a different water source, filter effluent from the Robert E. McQaude Water Treatment Plant in Andover, MA (28). This plant treats a blend of pond water and Merrimack River water. The process includes ozonation, alum coagulation, flocculation, settling, and GAC/sand filtration. These data were developed from bench scale experiments similar to the experiments used to develop the calibration data set. Details pertaining to the Andover data set are presented in Table 5. Only the parameters describing initial NOM site, chlorine, THM, and HAA concentrations were adjusted to fit the model to the Andover data set. The values of the parameters listed in Table 3 were not changed. Goodness of fit parameters for the Andover data set are presented in Table 6. Table 7 shows TOC and UV absorbance values for waters used in this work with corresponding model parameters.

Conclusions

A model based on a simplified conceptual reaction mechanism that predicts chlorine decay and the formation of THMs and HAAs was developed and calibrated. The form of the model is a system of differential equations (solved numerically), including fifteen adjustable parameters. Two of these parameters represent reactive site concentrations within the NOM molecules, and are site specific. The other parameters are rate constants and distribution factors that are expected to be more general. In this work, limited testing of the model was performed where the rate constant parameters were calibrated and the model applied to waters from a different source (of similar quality to the calibration source) with good results. We have found the proposed model particularly useful for distribution system modeling where the model was initially calibrated using water from the same source, and only the two NOM site parameters are adjusted to reflect changes in NOM concentration and quality over time.

Table 5. Robert E. McQuade WTP: Bench scale bottle test experiments.

Date

Sample

Collected

 

 

Set

 

 

N1

Cl2

Dose

(mg/L)

 

Temp.

(° C.)

 

 

pH

 

 

[NOM]2

6/97

0

10

2.5

20

9

1

 

1

7

1.25

20

9

1

 

2

9

2

20

9

1

 

3

9

3

20

9

1

 

4

9

2.5

8

9

1

 

5

9

2.5

15

9

1

 

6

9

2.5

20

8

1

 

6

9

2.5

20

8

1

 

8

9

2.5

20

8.5

1

 

9

9

2.5

20

9

0.5

7/97

0

9

2.5

20

9

1

 

1

9

2

20

9

1

 

2

9

2.5

20

8

1

 

3

9

2.5

9

9

1

 

4

7

2.5

20

9

0.5

1 number of individual observations

2 fraction of undiluted concentration (varied by dilution with deionized water)

Future Work. The calibration and test data sets were both developed using low-bromide waters, and the proposed model does not include bromide effects. The presence of bromide is expected to have a substantial affect on both the speciation and total formation of THMs and HAAs. Use of the model with waters containing substantial bromide concentrations might therefore require further refinements.

As stated above, "instantaneous" (in the time scale of minutes to days) byproduct formation and chlorine demand are treated as constants in the proposed model. Representation of instantaneous formation as a constant is based on the assumption that the total instantaneous demand and formation from fast-reacting NOM sites remains constant for different environmental conditions, although the kinetics may be different. This assumption may not be valid for all waters, and it should be noted that instantaneous chlorine demand and byproduct formation may represent a substantial fraction of the total. A more detailed representation of fast reactions in the model might therefore be required in some cases.

 

Table 6. Andover data set fit.

Parameter

Value

Number of data points

491

Sum of squared observations

613

Sum of squared deviations

38.5

R2adj

0.934

 

Table 7. NOM characteristics, "instantaneous" byproduct formation, and initial site concentrations.

 

Water Source

NOM Characteristics

Initial NOM site concentrations

"Instantaneous" byproduct formation

TOC

(mg/L)

UV 254

(cm-1)

S1o

(mM)

S2o

(mM)

THMo

(mM)

DCAAo

(mM)

TCAAo

(mM)

Calibration Set A1

1.91

0.030

1.027

8.00

0.054

0.071

0.051

Calibration Set B1

2.11

0.027

1.14

6.32

0.070

0.040

0.017

Calibration Set C1

2.08

0.028

1.27

7.25

0.054

0.074

0.047

Andover Set 12

1.73

0.033

0.617

1.79

0.040

0.031

2.2e-3

Andover Set 22

1.73

0.033

0.335

2.24

0.035

0.036

5.9e-3

1Lake Gaillard Water Treatment Plant, North Branford, CT-South Central CT Regional Water Authority

2Robert E. McQuade Water Treatment Plant, Andover, MA-Town of Andover

3Typical value-measured value for sample not available

 

Acknowledgements

The funding for this research provided by the South Central Connecticut Regional Water Authority is gratefully acknowledged. The authors would also like to thank John Affinito, Tom Whitbread and Jeff Johnson at the Lake Gaillard Water Treatment Plant and John Pollano at the Robert E. McQuade Water Treatment Plant for their cooperation in providing water samples used in this work.

Acronyms

BCAA bromochloroacetic acid

DCAA dichloroacetic acid

DBP disinfection byproduct

DHAA sum of di-halogenated HAA species

HAA haloacetic acid

NOM natural organic matter

TCAA trichloroacetic acid

THAA sum of tri-halogenated HAA species

THM trihalomethane

TOC total organic carbon

TTHM total trihalomethane (sum of four species)

USEPA United States Environmental Protection Agency

UV ultra-violet

List of Symbols

a 1,THM a 2,THM a 1,TCAA a 2,TCAA a 1,DCAA a 2,DCAA

factors relating byproduct formation and NOM site consumption

aHOCl, aOCl-

pH-dependent distribution factors for the chlorine species

a 1P, a 2P

distribution factors accounting for pH and oxidant concentration effects on byproduct speciation

b12,THM, b22,THM, b1,TCAA, b11,TCAA, b21,TCAA, b1,DCAA, b2,DCAA

factors representing the fractional contributions of NOM site classes, and uncatalyzed, oxidation, and hydrolysis pathways to the formation of individual byproduct species

q 1, q 2f, q P

rate adjusting coefficients for temperature effects

[Cl2]

free chlorine concentration

[HOCl], [OCl-]

hypochlorous acid, hypochlorite concentrations

[S1], [S2H], [S2-]

NOM site concentrations

k1, k21f, k21r, k22

rate constants

k¢ 1, k¢ 21f, k¢ 21r, and k¢ 22

apparent rate constants

kP, kP,OH, kP,HOCl

coefficients representing the relative importance of uncatalyzed, hydrolysis, and oxidation pathways in byproduct formation

n1, n2

factors relating chlorine demand and NOM site consumption

R1, R21f, R21r R22

reaction rates

T, Tref

Temperatures

R2adj

adjusted coefficient of multiple determination

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