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Chapter 5

An Economical Experimental Approach to Developing Disinfection By-Product Predictive Models

Downloaded by GEORGETOWN UNIV on August 24, 2015 | http://pubs.acs.org Publication Date: November 19, 1996 | doi: 10.1021/bk-1996-0649.ch005

R. Hofmann andR.C.Andrews Department of Civil Engineering, University of Toronto, 35 St. George Street, Toronto, Ontario M5S 1A4, Canada

Disinfection by-product (DBP) formation models were developed from bench-scale experiments using a fractional factorial design, with no replicates. This experimental approach minimizes the amount of data required to develop a model while sacrificing some precision. Despite the lower precision, the resultant models still accounted for the majority of the variation in the observed data. This method may be employed to develop site-specific DBP formation models with maximum economy.

Anticipated lower limits on disinfection by-products (DBPs) in drinking water may force certain water treatment utilities to develop strategies which will minimize DBP formation. A model that predicts DBP concentrations, given water quality characteristics and disinfection parameters, would be a useful tool for this purpose. Researchers have identified this need and have attempted to develop such models. For example, two studies led to the development of total trihalomethane (TTHM) and haloacetic acid (HAAg) predictive models, respectively (7, 2). These studies both involved bench-scale experiments using water samples obtained from many sites in the United States, which represented a cross-section of water types. The DBP formation data obtained from the different water sources were then combined into a single model. While such an approach is useful for illustrating overall trends in DBP formation, the resulting model will not, nor is intended to, always accurately predict DBP concentrations for a specific site, partly due to an inability to characterize organic precursor material. If a specific water treatment facility has identified a need to predict DBP concentrations for alternative treatment scenarios, and if generic DBP models cannot provide adequate levels of accuracy, then the alternative may be to construct a site-specific DBP formation model based on bench-scale experiments.

0097-6156/96/0649-0063$15.00/0 © 1996 American Chemical Society

In Water Disinfection and Natural Organic Matter; Minear, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1996.

64

WATER DISINFECTION AND NATURAL ORGANIC MATTER

Objective This research represents a first step towards developing an experimental protocol that can be used to develop site-specific DBP formation models both quickly and economically. The objective of this work was to determine the feasibility of applying a factorial form of experimental design, using no replicates, to bench-scale experiments for developing site-specific DBP formation models.


Factorial Design Background The discussion provided herein concerning factorial design is intended only to provide the reader with a basic background. For more details, the reader is directed to a statistical reference text, such as Statistics for Experimenters (3). A factorial design may be used to quantify the effects of selected variables (factors) on a particular experimental outcome. In this case, the outcome is DBP formation, while the factors to be examined include pH, temperature, TOC, bromide concentration, disinfectant dose, and time. As an example, consider an experiment designed to quantify TTHM formation as a function of pH. The experimenter chlorinates a water sample at pH 6 in a bench-scale batch reactor, and following a selected contact time determines the TTHM concentration to be 50 μg/L. The experimenter simultaneously conducts a similar experiment at pH 8, and observes a TTHM concentration of 150 μg/L. Thus, the experimenter may perform a regression on the two data points, (pH 6, TTHM = 50 μg/L) and (pH 8, TTHM = 150 μg/L), to produce an equation which predicts TTHMs as a function of pH: TTHM ^g/L) = -210 + 45(pH)

(1)

The previous example is called a 2-level factorial design, since pH was varied between only 2 levels; a low level (pH 6) and a high level (pH 8). It should be noted that Equation (1) assumes that TTHM increases linearly with respect to pH. If the relationship is non-linear, then the equation is inaccurate. However, in order to investigate non-linearity, more experiments would be required. When several factors are being investigated (such as pH, temperature, TOC, etc.), the increase in the amount of experimental work in order to investigate non-linearity is geometric. For example, to investigate 3 factors, each at 2 levels, requires 2 =8 experiments, while investigation of 3 factors, each at 3 levels, requires 3 =27 experiments. Since the primary goal of this research was to develop an easy, economical means of developing site-specific DBP formation models, it was decided that investigations would be directed towards the use of 2-level designs rather than those of a higher level (i.e. 3- or 4- level designs). The argument for adopting this approach is that the extra accuracy associated with the higher level designs would not justify the much greater amount of work and cost involved. When investigating the effect of pH and temperature on TTHM formation, the general form of the resulting equation would be: 3

3


5.

HOFMANN & ANDREWS

Disinfection By-Product Predictive Models 65

TTHM = constant + pH effect + temp effect + (pHxtemp) interaction

(2)

Note that a factorial design also allows the identification and quantification of interactions between factors, as shown in an example experimental matrix for investigating 2 factors at 2 levels each (2 = 4 experiments total) (Figure 1). It is observed that at 10°C, an increase in pH from the low to the high level only results in 10 μg/L more TTHM, while at 20°C, the increase in pH results in an associated increase in TTHMs of 18 μg/L. Thus, the pH effect may be viewed as being temperature dependent (it can also be stated that the temperature effect is pH dependent). Such a dependence implies that there is a pHxtemperature interaction. The mathematics involved in quantifying interactions are not described herein; the reader is referred to a statistics text for a detailed explanation. In order to investigate the effects of η factors on a particular outcome (such as DBP formation), with each factor considered at 2-levels, 2 experiments would be required. For example, in Figure 1 pH and temperature are each varied between 2 levels, and therefore there are 2 =4 possible combinations. Consider the case where the influence of 6 factors on TTHM formation are to be investigated: 2 =64 experiments would be required. Each of the 64 experiments contributes to the estimation of 1 statistic which describes TTHM formation. Thus, with 64 experiments, an equation which describes TTHM formation as a function of 6 factors has 64 terms, as shown in Table I. A hierarchy exists with respect to the influence of the factor effects. Singlefactor effects are typically more significant than two-factor interaction effects, which in turn are more significant than three-factor interaction effects, and so on. Based on this information the experimenter can make certain assumptions which will lead to a reduction in the experimental workload, by making an informed assumption that the information which is lost is not significant. For example, in an experiment designed to investigate the effects of 6 factors on TTHM formation, with each factor evaluated at two-levels (2 ), the experimenter may choose to assume that all three-, four-, five-, and six-factor interactions are negligible. A model describing TTHM formation as a function of single-factors and two-factor interactions can then be constructed using only 16 experiments. This is called a fractional factorial design, and is denoted as 2 " , implying that a two-level investigation of six factors is accomplished in only 2 =16 experiments. The use of fractional factorial designs is a powerful way of reducing experimental work and cost, with limited loss of precision. The theory behind the construction of a fractional factorial design cannot be described in detail here. In the example previously described, where instead of conducting all 64 experiments only 16 were selected, this selection process is not random. It is based on a specific algorithm which can be found in an appropriate statistics text.


2

n

2

6

6

2

4

Determination of Experimental Error in Factorial Design. When investigating the effects of selected variables (i.e. pH, temperature) on a particular outcome (i.e. DBP formation), it is possible that some of the variables will not influence the outcome at all. It is also possible that the effects of certain variables are so small


66



10°C

pH6

pH9

/

\

20°C

25 μg/L

35 μξβ.

58 μΕ/L

I

l

TTHM Concentrations Predictive Equation: TTHM (μ§/1>) = 6 + 0.67(pH) - 0.1 (Temperature) + 0.267(pH)(Temperature) Figure 1. A 2 factorial design experiment to determine the effects of pH and temperature on TTHM formation.


HOFMANN & ANDREWS

Disinfection By-Product Predictive Models

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68


that they are not distinguishable from experimental error. An important part in developing a DBP formation model is detemining which factors are important enough to include in the model. For example, if the change in HAA concentration when varying pH from a low to high level was 2 μg/L, it must be determined whether pH was truly responsible for the observed change in HAAs, or whether the change was due to random error in the experiment. For this case the traditional way to distinguish real effects from random effects would be to determine the standard deviation of a series of HAA sample replicates, and then convert this information into a specific confidence interval. For example, replicate measurements of the same concentration of HAAs may reveal that 95% of the replicates will vary by ±3 μg/L. If this is the case, then the observed pH effect of 2 μg/L may simply be due to experimental error, and it may be inappropriate to include pH in an HAA formation equation. In order to make such judgments, the standard deviation of the DBP measurements mustfirstbe defined, which typically requires that replicate analyses be conducted. However an alternative method exists which can be used to estimate the experimental error in a factorial design without conducting replicates. A benefit of this approach is the minimization of the amount of experimental work required to develop DBP formation models. The estimation of experimental error when conducting a factorial (or fractional factorial) design is not presented in detail here, however a conceptual example is provided. Consider a 2-level factorially designed experiment to investigate the effects of 4 factors (pH, temperature, chlorine dose, and time) on TTHM formation. Thus 2 =16 combinations of the 4 factors are prepared as individual experiments, and the TTHM formation corresponding to each of the 16 combinations is measured. An initial hypothesis may be proposed that none of the 4 factors has an effect on TTHM formation. Therefore, it may be assumed that any variation in the 16 TTHM measurements is due to experimental error alone. Since experimental error is random, it should follow a Gaussian (Normal) distribution, and results from the 16 experiments can be examined to determine if they follow such a distribution. Suppose that 3 of the 16 measurements display a significant departure from the Gaussian distribution; this suggests that the particular combination of the 4 factors in those 3 samples had a real effect on TTHM formation. It can then be assumed that the remaining 13 experiments were unaffected by the 4 factors. The standard deviation and 95% confidence interval of the experimental error can be calculated from these 13 experiments which may now be viewed as replicates. Using the calculated 95% confidence interval, it can be determined if the 3 samples are, in fact, significantly affected by the 4 factors, or whether their observed TTHM concentrations were due to random error. Using this method, true factor effects can be distinguished from experimental error without conducting replicate experiments. The disadvantage of this approach is that the estimate of the experimental error is the sum of the scatter due to true experimental error plus the scatter due to real factor effects. Hence, this method overestimates experimental error, which may mask the smaller and mid-size effects. However, since the models being developed in this research are intended to provide information that can be used to develop DBP minimization strategies, it is the factors with the most significant effects on DBP 4


5. HOFMANN & ANDREWS

Disinfection By-Product Predictive Models

69

formation that are of practical interest, and it is these factors that are identified in a non-replicated factorial design.


Experimental Design Models which describe DBP formation were developed as a function of the following six factors: pH, disinfectant dose, contact time, total organic carbon (TOC), temperature, and bromide concentration. The selection of these variables included consideration of those which were known to affect DBP formation, as well as variables that can be routinely measured by a treatment facility. In particular, pH, disinfectant dose, TOC, and contact time, are parameters which may influence DBP formation, and can be controlled in a treatment train. Bromide concentration and temperature cannot be controlled, however these factors were included in the experiment to determine the sensitivity of the DBP predictive models to these two parameters. A series of models were developed using both raw and clarified water (see Methods section) from a surface water source. Models were developed which address both chlorine and chloramine application to clarified water, while only chlorine was added to the raw water. It was considered unnecessary to add chloramines to raw water, since chloramination is typically a secondary disinfectant and therefore normally not applied to raw water. An experiment based on a 2 " fractional factorial design, using no replicates, was conducted in order to examine the effects of the chosen six factors on the formation of AOX (adsorbable organic halides), four THMs, five haloacetic acids (monochloro-, monobromo-, dichloro-, dibromo-, and trichloro-), trichloronitromethane (TCNM), and dibromoacetonitrile (DBAN). A 2 design requires DBP formation to be measured in 16 different combinations of the variables. The combinations of the variables are shown in Table II. All experiments were conducted in bench-scale, batch reactors. 6

2

6-2

Methods The water used in this experiment was obtained from the Ottawa River, a large river located on the southern border of the provinces of Ontario and Quebec, Canada. Water quality characteristics of this river are summarized in Table III. Experiments were conducted using both raw and clarified water from this site. Clarification was performed in the laboratory, using an optimum alum dose as determined by turbidity reduction in a jar test, followed byflocculationusing a custom-built paddle at a standardized velocity gradient (G = 50 s"). The water was allowed to settle for 30 minutes prior to supernatant being decanted for use in an experiment. Sixteen 2.5L amber glass reactors were filled with either raw or clarified water and adjusted to the water quality characteristics dictated by the factorial design (Table Π). Samples were adjusted to pH 6.5 by the addition of a phosphate buffer, while samples at pH 8.5 involved the addition of a borate buffer. Buffers were prepared using Milli-Q water which contained the respective salts at near-saturation levels to minimize any dilution effects resulting from the subsequent addition of 1



70


buffers to the samples. High TOC levels corresponded to the initial TOC of the water samples; low TOC levels were achieved by diluting the samples with Milli-Q water using a 2:3 Milli-Q:sample volume ratio. Bromide concentrations were adjusted to the required levels by spiking with potassium bromide (low bromide levels corresponded to the ambient concentrations in the initial water samples). Temperature control was maintained by placing the reactors in temperature-controlled chambers. Chlorine stock solutions were prepared from commercially available Javex bleach, with the chlorine concentration measured prior to every experiment. Preformed chloramines were prepared between 15 to 90 minutes prior to addition to water samples by slowly adding a chlorine solution (pH 8.5) to an ammonium chloride solution at a C1 :NH -N mass ratio of 3:1. Thus, monochloramine was the only significant chloramine species present in the stock solution. The concentration of the resulting stock chloramine solution was always measured prior to addition to the water samples. All glassware was made chlorine demand free by exposure to a chlorine solution of at least 40 mg/L overnight in the dark. Standards for THMs, HAAs, HANs, and TCNM were obtained from Supelco, and used for calibration purposes within 1 week of receipt. The AOX standard stock solution was pentachlorophenol. All standards were stored at 4°C prior to use. Trihalomethanes, chloropicrin, and the haloacetonitriles were analyzed using a Hewlett Packard 5890 Series II Plus gas chromatograph, according to EPA Method 551 (4). Haloacetic acids were analyzed according to EPA Method 552 (5). Chlorine and chloramine residuals were measured using Standard Method 4500-C1 D (6). TOC was measured using Standard Method 5310 C (6). Bromide concentrations were determined using EPA Method 300.0 (7), with a Dionex DX500 ion chromatograph. 2

3

Results and Discussion Equations relating DBP formation to pH, TOC, time, disinfectant dose, bromide concentration, and temperature, as developed using a 2 " fractional factorial design with no replicates, are shown in Tables IV, V, and VI. Tables IV and V contain results which relate to the chlorination of raw and clarified water, respectively. Table VI shows results for chloramination of clarified water. The focus of this discussion is not the equations themselves, but rather whether or not a fractional factorial design approach using no replicates is capable of providing DBP formation models that may be readily applied. Therefore discussion of the experimental data focuses on the statistical parameters shown in Tables IV to VI, rather than the resulting equations. In these tables, R-squared values are shown, as well as the 95% confidence intervals of the estimate of the experimental error, as expressed by a percentage of the average DBP concentration. R-squared values provide measures of the percentage of the variation observed in the data that can be accounted for by the model. Hence, an R-squared value of 0.8 means that 80% of the overall variance of the data is described by the model. The remaining 20% is due to unidentified experimental error. Recall 6

2


In Water Disinfection and Natural Organic Matter; Minear, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1996. 6.5 8.5 6.5 6.5 8.5 6.5 6.5 6.5 8.5 8.5 8.5 8.5 6.5 6.5 8.5 8.5

24 24 24 24 1 1 1 1 1 1 24 24 24 1 24 1

5 8 8 5 8 8 5 8 8 5 8 5 8 5 5 5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

FACTOR

5 5 5 3 5 3 3 5 3 3 3 3 3 5 5 5

TOC (mg/L)

TEMPERATURE

CQ 1 20 20 20 1 20 1 1 20 1 1 20 1 20 1 20

BROMIDE

(mm 300 300 15 15 300 300 15 15 15 300 15 300 300 300 15 15

pH Color

29 TCU

7.3

< 10

TOC Bromide

3.4 NTU 5.9 mg/L

Turbidity

Table ΙΠ. Water Quality Characteristics of the Ottawa River Water. PARAMETER TYPICAL VALUE

H

RUN P

CONTACT TIME (hours)

Randomised 2 " Factorial Design Protocol.

DISINFECTANT DOSAGE (mg/L)

Table Π.


72


Table IV. DBP Formation Models for Chlorination of Raw Water. COMPOUND

95% Ct

EQUATION*

Trihalomethanes -214 + 1.14*Temp + 17.6*TOC - 0.10*Br + 24.3*pH+ 1.86*Time + 0.11*Temp*Time

0.93

13%

-4.48 + 0.15*Br + 0.84*Time

0.67

33%

CHBr Cl

-10.7 + 0.0029*Br - 0.056*Time 0.38*Br*Time

0.75

47%

CHBr3

0.60 + 0.010*Br

0.69

29%

TTHM

-31.5 + 3.5*Temp + 25.1*TOC + 30.5*pH + 3.6*Time

0.83

18%

CHCI3


CHBrCl

2

2

Haloacetic Acids MCAA

0.21 + 0.045*Temp + 0.10*Time

0.51

50%

DCAA

-19.8 + 1.0*Temp + 5.5*TOC + l.l*Time

0.82

17%

TCAA

67 + 8.1*TOC- 11.2*pH+ 1.3*Time

0.70

23%

MBAA

0.14 + 0.0070*Br

0.57

42%

DBAA

-0.26 + 0.1 l*Temp + 0.018*Br

0.73

28%

HAA

-45.0 + 2.0*temp + 14.2*TOC + 2.5*time

0.83

14%

AOX

-84.7 + 84.5*TOC + 8.12*Time

0.73

12%

DBAN

11.4 +0.01 l*Br- 1.30*pH

0.75

21%

TCNM

0.31 -0.0015*Br + 0.021*Time

0.53

59%

5

Miscellaneous

b

Units are as follows: All DBPs = Time = hours, Disinfectant dose = TOC = mg/L, Bromide concentration = Temperature = °C 95% CI = 95% confidence interval for the estimate of the experimental error, expressed as a percentage of the average DBP concentration.


5. HOFMANN & ANDREWS

Disinfection By-Product Predictive Modeh

Table V. DBP Formation Models for Chlorination of Clarified Water. EQUATION*

ie

95% Ct

-79.5 + 1.7*Temp - 0.096*Br + 13.7*pH + 1.7*Time

0.80

23%

-10.0 + 0.60*Temp + 0.096*Br + 0.69*Time

0.90

20%

COMPOUND Trihalomethanes CHCI3

CHBrCl

2

CHBr Cl

No Observed Factor Effects

N/A

85%

CHBr3

0.96 + 0.017*Br

0.62

29%

TTHM

-156 + 1.0*Temp + 12.0*TOC + 18.8*pH + 1.2*Time + 0.11 *Temp*Time

0.90

14%

0


2

Haloacetic Acids MCAA

No Observed Factor Effects

N/A

95%

DCAA

4.83 + 0.68*Temp + 0.68*Time

0.89

22%

TCAA

-11.5 + 0.50*Temp + 6.9*TOC - 0.034*Br + 0.89*Time

0.89

16%

MBAA

0.0043 *Br + 0.000292*Temp*Br

0.75

27%

DBAA

0.23 + 0.00066*Temp + 0.0012*Br + 0.0010*Temp*Br

0.84

33%

HAA

-23.3 + 1.4*Temp + 10.6*TOC + 1.7*Time

0.84

13%

AOX

-111 + 3.3*Temp + 62*TOC + 5.8*Time

0.93

8%

TCNM

-0.33 - 0.0019*Br + 0.019*Time

0.57

51%

5

Miscellaneous

16% 7.6 + 0.017*Temp + 0.014*Br - 0.85*pH + 0.93 0.00099*Temp*Br Units as follows: All DBPs = μβ/L, Time = hours, Disinfectant dose = TOC = mg/L, Bromide concentration = μg/L, Temperature = °C 95% CI = 95% confidence interval for the estimate of the experimental error, expressed as a percentage of the mean DBP concentration. None of the factors influenced the average DBP concentration by more than the 95% confidence level. DBAN

a

b

0


73

74


Table VI, DBP Formation Models for Chloramination of Clarified Water. COMPOUND

2

EQUATION*

B

95% Ct

1.05 - 0.015*pH*Time + 0.013*pH*Dose

0.51

10%

6.5 - 0.77*pH

0.74

33%

CHBr Cl

Below Detection Limits (

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