[Editor’s Note: This is an electronic reprint of the original document. Electronic copies of the original figures were not available, thus the original figures are not included in this report.]
The Sacramento-San Joaquin Delta is a source of drinking water for 20 million Californians. Because the Delta is part of a tidal estuary and its land use is predominantly agricultural, Delta waters tend to reflect high levels of bromides and organic material (Amy et al. 1990). Organics and bromides promote the formation of disinfection by-products (DBPs) in the presence of a strong oxidant. Trihalomethanes (THMs), one class of DBPs, are a suspected threat to human health when present in sufficient quantities in drinking water.
In 1979, the Environmental Protection Agency established a drinking water standard of 0.1 milligrams per liter for THMs. Anticipating revisions to the current standards and recognizing problems Delta water users may face in meeting more stringent requirements, DWR began a study of THM precursors in Delta waters. A conclusion drawn from that study was that revised THM regulations may necessitate modifications of drinking water treatment processes, modifications in the operation of Delta export facilities, or a combination thereof (DWR 1989). Besides THMs, the Environmental Protection Agency will be regulating a number of other DBPs. Those compounds most likely to be regulated include: trichloroacetic acid, dichloroacetic acid, total haloacetic acids, chloral hydrate, bromate, chlorate, and chlorite (Pontius 1991).
This chapter summarizes DWR's efforts to date in mathematically modeling THM formation potential (THMFP) in the Delta. The first section discusses current and upcoming publications related to this work. Future model enhancements, as identified in these publications, are briefly addressed. The second and third sections of this chapter present unpublished work that will be incorporated into the overall modeling framework.
The Division of Planning has recently published a report entitled Trihalomethane Formation Potential in the Sacramento-San Joaquin Delta: Mathematical Model Development (DWR 1991). The report documents DWR's initial efforts in modeling Delta THMFP. The contents of this report are summarized in two papers that will be published in the ASCE Journal of Water Resources Planning and Management (Hutton and Chung 1992a,1992b).
Two potential areas for future model enhancement were identified in the above publications. The first enhancement outlined below is applicable to existing and potential Delta export stations while the second enhancement is applicable to model boundary stations:
- Develop a correlation between THMFP values and expected tap water THM levels. The importance of such a correlation is that DWR's THMFP test assays the amount of precursor material in untreated source waters in the Delta, whereas drinking water standards for THMs apply only to treated drinking water. A methodology to predict THM concentrations in a water distribution system from THMFP data is presented in the last section of this
- Develop boundary conditions that relate DWR's precursor simulation parameter, TFPC (total THMFP as carbon), with a direct precursor measure. The importance of developing these boundary relationships is that TFPC is not well-suited for real time simulation, as a 7-day THMFP test must be performed to estimate its value at each boundary. A statistically-based precursor measure that has been proposed by Amy et al. (1987) is the product of total organic carbon (TOC) and ultraviolet absorbance at 254 nm (UVA), where TOC quantifies precursor concentration and UVA quantifies precursor reactivity in forming THMs. Work will commence on developing boundary relationships between TFPC and TOCxUVA as more data becomes available.
The following section summarizes a model enhancement that has been developed this past year and was completed subsequent to the publications discussed above.
Bromine Distribution Factors: Modified Formulation
Hutton and Chung (1992a,1992b) presented a mathematical model designed to
analyze source water management alternatives in the Delta, with a specific focus
on THMFP. Two empirical relationships were developed by the authors to describe
impacts of bromide on the distribution of compounds measured by DWR's THMFP
test. These relationships were based on 2000 samples of Delta channels and
agricultural drains collected in the Delta between 1983 and 1990 under DWR's
Municipal Water Quality Investigations (MWQI) program.
One empirical relationships, the Bromine Incorporation Factor, was originally
defined by Gould et al. (1981) as the following dimensionless term:
η = Bromine Incorporation Factor, 0 £ η
N = number of bromide atoms in THM compound
The second empirical relationship developed by the authors was the Bromine
Distribution Factors (S), a term defining a
vector of THMFP species distribution functions:
S = [s0(η), s1(η),
s0 = CHCl3 Distribution Factor = [CHCl3] / [THMFP]
s1 = CHCl2Br Distribution Factor = [CHCl2Br]
s2 = CHClBr2 Distribution Factor = [CHClBr2]
s3 = CHBr3 Distribution Factor = [CHBr3] / [THMFP]
Assuming functional forms dependent on η, Hutton and Chung (1992a)
performed regression analyses on the MWQI data set to derive model coefficients
that statistically describe the Bromine Distribution Factors. The resulting vector
of distribution functions, SR, is
given below in Eqs. 3a-3d:
SR was verified against a THMFP data set developed
under varying reaction conditions by Amy et al. (1987). An excellent
correspondence was observed between SR
and this data set, indicating that THMFP species distribute in a predictable
fashion under varying test conditions (DWR 1991).
Some caution is necessary in the use of SR,
however, as its predictions are not always constrained within the implied limits
of distribution functions. For instance, Eqs. 3a and 3b give negative
predictions at high values of η. But by definition, the functions should
always be greater than or equal to zero. Also, as shown in Fig. 1, the sum of
Eqs. 3a-3d is not equal to one for all values of η. But again by
definition, the sum of the distribution functions should always equal one. The
conditions cited above are not always satisfied because model
coefficients were determined statistically, with the objective being to minimize
sum-of-squares errors. Hutton and Chung (1992a) documented a simple approach to
adjust the values predicted by SR.
A technique is presented in this section that solves analytically for Bromine
Distribution Factor coefficients. A number of solution conditions are introduced
to eliminate the need for aposteriori adjustments of model predictions. Solution
results are evaluated by comparing predicted values with observed values from
the MWQI data set and other THM data sets.
A third order polynomial function dependent on η was assumed for each
Bromine Distribution Factor such that:
||i = 0, 1, 2, 3
Sixteen equations are required to arrive at a unique solution for the 16
unknown coefficients implied by Eq. 4. Ten conditions were identified to solve
for the unknowns:
||at h = 3
||at h = 0
||at h = 3
||at h = 1
||at h = 0
||at h = 3
||at h = 2
||at h = 0
Although only ten conditions are identified above, a unique solution can be
found. Eqs. 5i and 5j are valid over the entire range of η, suggesting that
these conditions can be employed to derive more than one equation. For
example, Eqs. 5b and 5e are obvious restatements of Eq. 5j. Eq. 5j was derived
by substituting Eqs. 2b-2e into Eq. 1.
The sixteen unknown coefficients were solved for in four steps: (i) First,
Eqs. 5c and 5d were employed to solve for b1 and c1 in
terms of a1. Per Eq. 5b, d1 = 0. (ii) Next, Eqs. 5f and 5g were
employed to solve for b2 and c2 in terms of a2.
Per Eq. 5e, d2 = 0. (iii) Substituting results from the previous steps into Eq.
5j, s3 coefficients were solved for in terms of a1 and a2.
A solution was found for a1 by employing Eq. 5h. (iv) Again,
substituting results from the previous steps into Eq. 5i, s0
coefficients were solved for in terms of a2. A solution was found for
a2 by employing Eq. 5a.
The resulting vector of theoretically-derived distribution functions, ST,
is given below in Eqs. 6a-6d:
Although ST satisfies the
conditions stipulated in Eqs. 5a-5j, it does not provide a good fit to observed
data. Fig. 2 shows the theoretical solution superimposed on the MWQI data set.
Figs. 3 and 4 show similar deviations between predicted and observed values,
with Fig. 3 illustrating THMFP data developed by Amy et al. (1987) and Fig. 4
illustrating a simulated distribution system (SDS) THM data set developed by the
Metropolitan Water District of Southern California (MWD). MWD's SDS THM test is
described by Koch et al. (1991).
As discussed above, the theoretical solution vector, ST,
does not provide a good fit to the Bromine Distribution Factor data sets.
Comparison of SR with ST
gives some insight into shortcomings of the theoretical conditions. Alternate
conditions were developed from this comparison to arrive at a modified solution
Not all of the theoretical conditions correspond with statistical
characteristics of the MWQI data set. Regression analyses suggest that s1
and s2 reach maximum values at somewhat
different values of η than specified in the theoretical conditions.
Likewise, areas under the theoretical curves deviate from the areas under the
regression curves. Integrating Eqs. 6a-6d reveals that the theoretical conditions
produce four identical areas of 0.75. Areas under the regression curves, in
contrast, are not equivalent. Integrating Eqs. 3a-3d results in the following
areas: 0.86 for s0, 0.59 for s1, 0.70 for s2,
and 0.83 for s3. This observation may suggest that a chemical
preference exists for the formation of chloroform (CHCl3) and
bromoform (CHBr3) over the other THM species, a consideration that
was not modeled by the theoretical conditions.
One means of improving the data fit of the theoretical solutions is to assume
a fourth order polynomial function for each Bromine Distribution Factor. Such an
approach allows for the incorporation of additional conditions that describe
data characteristics, e.g. maximum functional values or integrated functional
values. Although valid, this approach was not employed because of its reliance
on a more complex functional form. Instead, the third order functional form (Eq.
4) was maintained and the following 16 modified conditions were introduced with
the purpose of improving fit to the MWQI data set:
||at h = 0
||at h = 3
||at h = 3
||ath = 0
||ath = 3
||at h = 1.05
||at h = 0
||at h = 3
||at h = 1.90
||ath = 0
||ath = 3
||at h = 0
Eqs. 7g and 7k are modified conditions that address deviations between the
location of maximum values of s1 and s2. Eqs. 7d, 7h, 7l
and 7p are modified conditions that address deviations between areas under the
functional curves. These latter conditions also satisfy the integrated forms of
Eqs. 5i and 5j:
The sixteen modified conditions (Eqs. 7a-7p) were employed to solve for 16
new coefficients. The resulting vector of modified distribution functions, SM,
is given below in Eqs. 10a-10d:
SM always gives predictions that lie within a
meaningful distribution function range of zero to one. Furthermore, the
distribution factor sum is always equal to one. Hence, predictions from SM
do not require aposteriori corrections.
Verification of Modified Solution
The modified solution vector, SM,
was verified against the original MWQI calibration data as well as the THMFP
data set developed by Amy et al. (1987) and the SDS THM data set developed by
MWD. SM is superimposed on these
data sets in Figs. 2, 3 and 4. These figures show an excellent correspondence
between the modified solutions and the data sets, indicating that SM
is an appropriate model for the Bromine Distribution Factors under a variety of
An analytical solution scheme was employed to solve directly for Bromine
Distribution Factor model coefficients. The Bromine Distribution Factors have
been shown elsewhere to be useful in characterizing the impact of bromide on the
distribution of THMFP compounds (Hutton and Chung 1992a,1992b). The modified
relationships are superior to those calibrated from regression analyses in that
their predictions are always constrained within meaningful limits. These
modified relationships were verified against three data sets that reflect a wide
spectrum of water quality and reaction conditions.
Because the Bromine Distribution Factor functions have been shown to provide
consistently good predictions over a wide range of water quality and reaction
conditions, these relationships provide a potential link in developing
correlations between data collected to measure precursor levels (i.e. high
chlorine dose THMFP data) and data collected to estimate THM levels at the
consumer's tap (i.e. SDS THM data). Employing the Bromine Distribution Factors
and other relationships to correlate DWR's THMFP data with SDS THM data is
discussed in the next section.
Correlating THMFP Data With SDS-THM Data
Measuring the tendency of water to form THMs or other DBPs is usually
undertaken to accomplish one of two important objectives, either to estimate the
total concentration of precursor material in a source water or to estimate the
extent to which these precursors yield THMs at the consumers' tap. The former
objective, associated with evaluating precursor removal strategies and source
water management alternatives, can be accomplished with a fixed high-chlorine
dosage (high-dose) THMFP test. The latter objective, associated with evaluating
DBPs likely to be formed under actual water treatment conditions, can be
accomplished with a variable low-chlorine dosage (low-dose) THMFP test or a
site-specific SDS test.
Design aspects of high-dose THMFP assays and SDS tests (or low-dose THMFP
tests) reflect their differing objectives. To allow for unbiased comparisons of
data between locations or periods of interest, standard conditions are of
primary importance in high-dose assays. High chlorine doses minimize the
differences in chlorine residual from one sample to another, and as observed by
Reckhow and Edzwald (1991), assay values are independent of chlorine residual at
high residual values. SDS tests, on the other hand, must be tailored to specific
treatment systems and must reflect specific disinfection conditions (Reckhow and
Edzwald 1991). At chlorine residuals typically employed during water treatment
and distribution, THM formation is dependent on residual levels.
Given the differing objectives and design aspects of SDS tests and high-dose
THMFP tests, it is not surprising that these tests provide information that is
readily correlated only in a qualitative sense. Yet water supply decisions must
ultimately consider how source water precursors translate into tap water quality
for a given level of treatment. Recognizing the importance of understanding this
relationship in the Delta, the California State Water Resources Control Board
(1991) identified the need to develop a correlation between THMFP monitoring
data and THM concentrations in treated drinking water. To provide such a link,
this section presents a framework that correlates THM data collected under
different reaction conditions. The framework is specifically employed to develop
two models: one that predicts 24-hour SDS concentrations from 3-hr SDS
measurements and one that predicts 24-hour SDS concentrations from high-dose
THMFP measurements. The purpose of the former model is to provide a means of
estimating distribution system THMs from treatment plant measurements. The
purpose of the latter model is to provide a means of estimating distribution
system THMs from source water precursor measurements. Correlation objectives are
presented schematically in Fig. 5. Emphasis is placed on predicting THMs in a
distribution system because this location is the best indicator of tap water
quality. In addition to model development, model verification and applicability
to source water management is also discussed.
Three data sets are employed in this study. The first data set represents
high-dose THMFP measurements. The latter data sets represent SDS measurements.
Of these, one was developed to simulate chlorine contact time in a treatment
plant (3-hour SDS data) and the other was developed to simulate chlorine
contact time in a water distribution system (24-hour SDS data).
High-Dose THMFP Data
DWR utilizes a high-dose THMFP test to assay precursor levels in Delta
waters. Prior to the test, samples are filtered through a 0.45 millipore
membrane filter. Filtration has only a minor impact in terms of precursor
removal (DWR 1989). Samples are then subjected to a fixed free chlorine dose
of 120 mg/L and incubated for a seven day period at 25°
C. Finally, the samples are dechlorinated using sodium thiosulfate and
analyzed by the gas chromatograph purge and trap method. DWR found a high
chlorine dose to be necessary in meeting demands exerted by agricultural drain
samples, waters which tend to contain exceptionally high levels of organic
precursors. High chlorine residuals are consistently produced by the THMFP
test, suggesting that the precursor assay is independent of chlorine residual
(Reckhow and Edzwald 1991). Samples are not buffered to a fixed pH value
during the test.
Samples have been collected monthly by DWR from 17 tributaries and channels
in the Delta since 1983. Sample locations are shown in Fig. 6. Two of the 17
locations -- Sacramento River at Greene's Landing and Banks Pumping Plant --
are also employed by MWD as SDS sample locations. Therefore, parallel SDS and
high-dose THMFP test values are available at these two locations. Parallel
data collected between November 1990 and August 1991 are utilized in this
study to correlate high-dose THMFP and SDS THM values.
To study chlorine disinfection by-products formation in their finished
waters, MWD is collecting SDS data from the California State Water Project (SWP)
and the Colorado River Aqueduct. In developing these data, samples are first
jar treated to simulate treatment plant coagulation, flocculation,
sedimentation and filtration. Samples are dosed with polymer and alum during
jar treatment to minimize effluent turbidity; this chemical dosing also
results in a reduction in precursor levels.
After jar treatment, samples are chlorinated and incubated for 3 and 24
hours to simulate contact time in a treatment plant and in a water
distribution system, respectively. The 3-hour samples are dosed to maintain a
free chlorine residual of approximately 1.0-1.5 mg/L and the 24-hour samples
are dosed to maintain a residual of approximately 0.5-1.5 mg/L. Temperature is
fixed at 25° C (summer conditions) and pH is
buffered at 8.2 for both the 3-hour and 24-hour data sets. Details on MWD's
SDS test are provided by Koch et al. (1991).
Forty-seven (47) 3-hour and 24-hour samples were collected between November
1990 and August 1991 at six sites within California. These sites are located
in Fig. 7.
Three statistical relationships are presented to correlate THM data collected
under different reaction conditions. The first statistical relationship, total
THM formation, addresses the impact of reaction conditions on precursor
oxidation. The second and third statistical relationships, Bromine Incorporation
Factor and Bromine Distribution Factors, address the impact of ambient water
quality and reaction conditions on THM halogenation. When these relationships
are employed within the framework discussed below and diagrammed in Fig. 8,
individual THM species formation under one set of reaction conditions may be
estimated from the THM formation measured under a different set of conditions.
Total THM Formation
The first statistical relationship employed within the framework is between
total THM formations measured under reaction conditions of interest. To develop
such a relationship, parallel tests must be performed on the same water sample.
Reckhow (1984) observed a proportional relationship between 3-day and 7-day
high-dose THMFP concentrations. Reckhow and Edzwald (1991) observed the ratio of
low-dose to high-dose THMFP concentrations to vary with precursor concentration.
In this study, total molar THM formations were observed to relate
proportionally, suggesting a model form:
where [TTHM]Y is the total molar concentration under condition "Y"
and [TTHM]X is the total molar concentration under condition
"X". An intercept is excluded from Eq. 11, as [TTHM]Y
should approach zero as [TTHM]X approaches zero. If the objective is
to develop a statistical relationship that estimates SDS values from measured
THMFP values, the model constant in Eq. 11 would be derived by correlating SDS
data (condition "Y") with THMFP data (condition "X"). The
magnitude of the model constant is influenced by the relative difference in
reaction conditions such as temperature, chlorine dose, pH and reaction time.
Bromine Incorporation Factor
A second relationship, Bromine Incorporation Factor, must be established for
the predicted reaction conditions, or condition "Y" following the
above convention. Using the same example, if the objective is to develop a
statistical relationship that estimates SDS values from measured THMFP values,
the relationship must be developed from SDS data.
Gould et al. (1981) defined the Bromine Incorporation Factor, η, as a
dimensionless term to describe the aggregate speciation of a given water sample.
This term is defined as the molar THM concentration as bromide divided by the
total molar THM concentration (see Eq. 1). When η approaches zero, the
molar distribution of THM species is predominantly chloroform, the THM compound
with zero bromide atoms. When η approaches three, the molar distribution of
THM species is predominantly bromoform, the THM compound
with three bromide atoms. At intermediate values of η, a balanced
distribution of THM compounds is indicated.
Hutton and Chung (1992a) found the Bromine Incorporation Factor to be related
to a surrogate bromide:precursor ratio in Sacramento-San Joaquin Delta waters
under high-dose THMFP reaction conditions:
||k = bromine saturation level = 3
||α = [Cl-]/[THMFP] (mM/μM)
||β = regression constant = 5.48
This relationship was developed from 2000 high-dose THMFP measurements
collected by DWR (1989,1990a,1990b) and verified with data collected under
similar reaction conditions. Several empirical model forms were investigated by
To compensate for limited bromide data (bromide was not measured by DWR until
May 1990), a decision was made to employ chloride as a surrogate measure of
bromide in modeling the Bromine Incorporation Factor. By employing this
surrogate measure, a consistent spatial distribution of chloride and bromide in
the Delta is implicitly assumed. The ionic ratio has been observed to be most
consistent in the western Delta where tidal influences are important and less
consistent in agricultural drains and in the northern Delta where seawater
influences are less significant. Agricultural drains and channels in the
northern Delta have not generally demonstrated
significant bromide effects in THM formation (i.e. low values of α),
thereby minimizing any potential discrepancies (Hutton and Chung 1992a).
Expressing the numerator and denominator of α in molar units eliminates the
bias of comparing THM compounds with different bromine fractions, thereby
reflecting the relative amount of bromide and carbon precursor.
Bromine Distribution Factors
Eqs. 10a-10d were employed in this study to represent the Bromine
Distribution Factors. Recalibration was not necessary, as these relationships
have been shown to provide consistently good predictions over a wide range of
water quality and reaction conditions (see Figs. 2-4).
Model Calibration #1: Correlating SDS Data Sets
The correlation framework presented in Fig. 8 was first applied to develop a
model that predicts 24-hour SDS concentrations from 3-hour SDS measurements.
Relationships were calibrated for total molar THM formation and Bromine
Incorporation Factor. As a preliminary analysis of the model, these
relationships were employed in conjunction with Eqs. 10a-10d to predict 24-hour
SDS concentrations from the 3-hour SDS calibration data. This analysis is
considered to be preliminary because a true model verification should be
accomplished with data other than those used for calibration.
Total THM Formation
Total molar THM formation correlation was excellent between the 3-hour
samples and the 24-hour samples. The relationship, determined by linear
regression and given in Eq. 13, has a r2 value of 0.98 (see Fig. 9).
||[TTHM]24-hr = 1.834 [TTHM]3-hr
As expected, Eq. 13 reflects more oxidation of precursor material to THMs
after 24 hours because of longer chlorine contact times. Eq. 13, which is based
on 47 observations, suggests that total THM formation nearly doubles with the
increased contact time.
Bromine Incorporation Factor
To predict Bromine Incorporation Factor, 24-hour SDS data was fit by
nonlinear regression to the model form given in Eq. 14, resulting in a r2 value
of 0.98 (see Fig. 10).
||α* = [Br-]/[TTHM]24-hr (μM/μM)
||β* = regression constant = 7.69
||γ = regression constant = 1.38
In addition to providing a good match to the data, a rational basis exists
for selecting this model form. Population growth tends to follow a pattern
similar to Eq. 14. Analysis of such growth has revealed that the rate of growth
is initially proportional to the size of the population. Later, however, some
limiting factor (such as space or food) begins to decelerate growth until a
saturation level is reached. Bromine incorporation into THM species can be
thought to follow a pattern analogous to population growth, with bromine (HOBr)
being analogous to the "population" and organic precursor (THM
molecules) being analogous to the "space" or "food".
Initially, for a fixed set of reaction conditions and a fixed concentration of
precursor material, bromine incorporation is proportional to the natural
logarithm of bromide concentration. But as bromination progresses, the number of
available molecular reaction sites become limiting. Finally, a saturation level
is approached as three bromine atoms are associated
with each THM molecule (i.e. η=k=3).
It is interesting to note that, when γ=1, the model form of Eq. 14
reduces to the model form presented in Eq. 12. Eq. 14 deviates from Eq. 12 in
that a) bromide is used instead of a chloride surrogate in the molar ratio,
and b) the molar ratio is dimensionless.
Preliminary Model Analysis
Following the steps outlined in Fig. 8, the 3-hour SDS calibration data were
employed to predict 24-hour SDS species concentrations. Total molar THM
concentrations were transformed from 3-hour values
to 24-hour values with Eq. 13. Transformed molar values were used in conjunction
with observed molar bromide concentrations to predict η per Eq. 14. Bromine
Distribution Factors were then estimated per Eqs. 10a-10d. Finally, individual
species concentrations were calculated as the product of the total molar THM
concentrations times the respective distribution factors times the respective
Results from the preliminary model analysis are presented in Fig. 11 and show
predicted versus observed 24-hour SDS species concentrations. The close
comparisons between predicted and observed values indicate a good model
Model Calibration #2: Correlating SDS & THMFP Data
Next, the correlation framework was applied to
develop a model that predicts 24-hour SDS concentrations from high-dose
precursor concentrations, i.e. 7-day THMFP samples. A relationship was
calibrated for total molar THM formation but not for η. Eq. 14 serves as a
useful relationship for Bromine Incorporation Factor as the objective is
to predict 24-hour values. Similar to the previous calibration discussion, a
preliminary model analysis is presented.
Total THM Formation. A poorly-defined linear relationship between 24-hr SDS
formation and THMFP is given in Eq. 15 and shown in Fig. 12.
||[TTHM]24-hr = 0.197 [THMFP]
Eq. 15, which has a r2 value of 0.66 and is based on 18
observations, suggests that total molar THM formation under the high-dose THMFP
conditions is nearly five times that of the formation under 24-hour SDS
conditions. The observed increase is attributed to a longer reaction time and a
higher chlorine dose.
Much of the data scatter shown in Fig. 12 is attributed to variation in
precursor removal during SDS jar treatment. As suggested by Amy et al. (1987),
precursor concentration in the SDS samples can be defined as the product of TOC
and UVA, where TOC is related to precursor quantity and UVA is related to
precursor reactivity. Fig. 13, which compares model fit to the level of SDS
precursor removal, shows that Eq. 15 tends to (1) underpredict 24-hour formation
at lower fractions of precursor removal and (2) overpredict 24-hour formation at
higher fractions of precursor removal. To account for precursor removal
variations in the SDS test, the dependent variable in Eq. 15 was modified such
||[THMFP]* = [THMFP] (1-R).542
where R is the precursor removal fraction resulting from SDS jar treatment.
Based on observations that THM formation is related to precursor concentration
as a power function (Amy et al. 1987), the exponent in Eq. 16 was determined by
comparing [THMFP] values and raw water precursor values (TOCxUVA) on a log-log
plot. [THMFP]* represents the expected high-dose THMFP of a water
subjected to precursor removal by jar treatment.
Another linear regression was performed, resulting in the following
||[TTHM]24-hr = 0.341 [THMFP]*
Eq. 17, shown in Fig. 14, provides a much better fit to the data and has an r2
value of 0.89. Eq. 17 suggests that, for the same amount of precursor material,
total THM formation increases by a factor of three with increased reaction time
and chlorine dose.
Another potential source of data scatter, in addition to precursor removal
variation, is pH variation associated with DWR's unbuffered THMFP test.
Unfortunately, the impact of pH variation cannot be evaluated at this time as it
is not being measured by DWR. Chlorine residual is another varying factor in
DWR's THMFP test. However, observations by Reckhow and Edzwald (1991) suggest
that at high chlorine residuals (such as those produced by DWR's test), assay
results are independent of chlorine residual. Because Eq. 17 is based on limited
sampling, correlation "strength" or "weakness" is not
conclusive at this time.
Preliminary Model Analysis. Again following the steps outlined in Fig. 8, the
THMFP calibration data were employed to predict 24-hour SDS species
concentrations. Total molar THM concentrations were transformed from THMFP
values to 24-hour values with Eq. 17. Transformed
molar values were used in conjunction with observed molar bromide concentrations
to predict η per Eq. 14. Bromine Distribution Factors were then estimated
per Eqs. 10a-10d. Finally, individual species concentrations were calculated
as the product of the total molar THM concentrations times the respective
distribution factors times the respective molar weights.
Results from the preliminary model analysis are presented in Fig. 15 and show
predicted versus observed 24-hour SDS species concentrations. Again, close
comparisons between predicted and observed values indicate a good preliminary
Limited data does not permit a thorough model verification at this time.
However, three parallel observations provide a hint of the model's effectiveness
in predicting 24-hour SDS concentrations from high-dose THMFP measurements. Data
on SDS precursor removal is not available for these parallel observations;
hence, Eq. 15 is used instead of Eq. 17 to predict total THM formation.
Comparisons of model predictions and observed values, which look quite
promising, are summarized in Table 1 and are discussed below.
July 1989 Observations
In their verification of SDS results with observed distribution system
concentrations, Koch et. al. (1991) reported 14-hour and 24-hour SDS values
produced by raw influent water to MWD's Jensen Filtration Plant during July
1989. While all four THM species concentrations are reported for the 14-hour
sample (see column 4 of Table 1), only a total THM
concentration of 145 μg/L is reported for the 24-hour sample. During both
observations, influent to the plant was 100 percent SWP water. Banks Pumping
Plant supplies the SWP; hence, assuming additional precursor sources to the
SWP are negligible, THMFP measurements at Banks represent the precursor load at
Jensen. To account for an approximately one year travel and retention time
between Banks and Jensen, 12-month average THMFP and bromide values (see column
2) were calculated from observed data to predict SDS concentrations. Predicted
24-hour SDS values, given in column 3 of Table 1, compare favorably with the
observed 14-hour values in column 4. The total THM
value of 143 μg/L is nearly identical to the reported 24-hour value of 145
August 1990 Observations
Parallel THMFP and 20-hour SDS measurements were taken from samples collected
at Banks Pumping Plant and Greene's Landing on August 6, 1990. Predicted 24-hour
SDS values at Banks, given in column 6, compare reasonably well with observed
20-hour SDS values (see column 7) except for a substantial overprediction of
bromoform. Predicted 24-hour SDS values at Greene's, given in column 9, compare
closely with observed 20-hour SDS values (see column 10) except for a
substantial overprediction of chloroform. SDS precursor removal may be
influential in the differences between predicted and observed values. For
example, if precursor removal for the Greene's Landing SDS sample was 77% (R =
0.77), the correlation framework would predict SDS values nearly identical to
Application to Source Water Management
Hutton and Chung (1992b) reported the use of mathematical modeling techniques
to simulate the fate and movement of THM precursors in the Sacramento-San
Joaquin Delta. The authors presented model simulation results in terms of THMFP.
While THMFP gives much insight into precursor levels in source waters, it gives
only limited insight into typical finished drinking water quality. The framework
presented in this paper is well-suited for estimating drinking water THM
concentrations from such THMFP model results. Utility of the correlation
framework in evaluating source water management alternatives is illustrated with
a hypothetical problem defined as follows:
Due to concerns with THMs in treated water from the Sacramento-San Joaquin
Delta, operating strategies are modified and facilities are strategically
constructed so that salinity intrusion into the Delta from San Francisco Bay is
greatly reduced. The resulting water quality impact is as follows: Br- is
reduced from 0.51 mg/L (150 mg/L Cl-) to 0.17 mg/L (50 mg/L Cl-). Precursor
loads are not impacted by modified operations and facilities. What incremental
improvement in water quality, in terms of THMs, is expected at export locations?
This hypothetical problem is evaluated at three precursor levels (as measured
by high-dose THMFP) for the defined "base" and "plan"
conditions. In the first set of calculations, individual THM species are
expressed as high-dose THMFP concentrations. In the second set of calculations,
the correlation framework is invoked to express individual THM species as SDS
Fig. 16 summarizes THMFP values calculated for 3 precursor levels under base
and plan conditions. The plan condition results in a reduction of total THMFP
mass concentration by approximately 10 percent. While chloroform increased by 30
to 60 percent, all bromomethane species decreased dramatically: CHCl2Br
was reduced by 50 to 60 percent, CHClBr2 was reduced by 70 percent,
and CHBr3 was reduced by 90 percent.
Fig. 17 summarizes 24-hour SDS values calculated for the same precursor
levels and under the same base and plan conditions. A SDS precursor removal of
60% (R = 0.60) is assumed. The plan condition results in a reduction of total
THMFP mass concentration by approximately 20 percent. Chloroform increased
dramatically by approximately 400 to 900 percent and CHCl2Br
increased by 40 to 200 percent. CHClBr2 increased by 10 percent at
precursor level "I" and was reduced by 30 to 50 percent at the other
precursor levels. CHBr3 was reduced by 80 to 90 percent.
This hypothetical problem shows that, even when used within a context of
incremental analyses, the statistical relationships are very sensitive to the
type of data selected -- SDS or high-dose THMFP. Fig. 18 compares the
incremental variation in results from Figs. 16 and 17, focusing on precursor
level "II". While both analyses predict chloroform concentrations to
increase under plan conditions, the latter predicts a significantly larger
change on a percentage basis. A striking difference also exists between the CHCl2Br
estimates, with THMFP values showing an incremental decrease and SDS values
showing an incremental increase. And while both analyses predict CHClBr2
and CHBr3 concentrations to decrease under plan conditions, the
incremental decreases vary. Therefore, to estimate incremental responses in
drinking water quality to changes in source water quality even in a qualitative
sense, high-dose THMFP data should be transformed into equivalent SDS values.
A mathematical framework that correlates THM data collected under different
reaction conditions was presented. The framework was specifically employed to
develop two models: one that predicts 24-hour SDS concentrations from 3-hr SDS
measurements and one that predicts 24-hour SDS concentrations from high dose
THMFP measurements. The purpose of the former model is to provide a means of
estimating distribution system THMs from treatment plant measurements. The
purpose of the latter model is to provide a means of estimating distribution
system THMs from source water precursor measurements. This latter model is
particularily important to DWR, as an extensive amount of high-dose THMFP data
has been collected in the Sacramento-San Joaquin Delta since 1983. Emphasis is
placed on predicting THMs in a distribution system because this location is the
best indicator of tap water quality.
Model calibrations and verifications, although generally quite good, are
considered to be preliminary because of limited SDS data available for this
study. The models will be recalibrated and verified as more data becomes
available. The most significant aspect of the calibration exercise is that it
shows THM data collected under different reaction conditions can be related
mathematically. The preliminary calibration also reveals a need to account for
jar treatment precursor removal when comparing SDS measurements with THMFP
The correlation framework is also shown to be an important link in using
high-dose THMFP data to evaluate source water management alternatives. A
hypothetical problem illustrates that incremental analysis of alternatives is
extremely sensitive to the type of values employed, SDS or THMFP. This finding
is particularily important to DWR in its evaluation of management alternatives
in the Sacramento-San Joaquin Delta.
Overall Model Framework
Figure 19 schematically presents the current overall framework in modeling
THMFP of Delta waters and in estimating corresponding drinking water THM
concentrations. This framework employs the DWR Delta Simulation Model (DWRDSM)
to simulate fate and movement of bromide and THM precursors in conjunction with
the modified empirical relationships and correlations discussed in this chapter.
Amy, G.L., Chadik, Z.K. and Chowdhury, Z.K. (1987). "Developing
Models for Predicting Trihalomethane Formation Potential and Kinetics,"
Journal AWWA, 79(7),89.
Amy, G.L. et al. (1990), "Evaluation of THM Precursor Contributions
from Agricultural Drains", Journal AWWA, 82(1),57.
California Department of Water Resources (1989). The Delta as a Source of
Drinking Water: Monitoring Results 1983 to 1987.
DWR (1990a). Delta Island Drainage Investigation Report of the
Interagency Delta Health Aspects Monitoring Program: A Summary of
Observations During Consecutive Dry Year Conditions, Water Years 1987 and
DWR (1990b). Project Report of the Interagency Delta Health Aspects
Monitoring Program (Municipal Water Quality Investigations Program): Summary
of Monitoring Results January 1988 - December 1989.
DWR (1991). Trihalomethane Formation Potential in the Sacramento-San
Joaquin Delta: Mathematical Model Development, Division of Planning.
California Water Resources Control Board (1991). Water Quality Control
Plan for Salinity: San Francisco Bay / Sacramento-San Joaquin Delta Estuary,
Gould, J.P., Fitchhorn, L.E. and Urheim, E. (1981). "Formation of
Brominated Trihalomethanes: Extent and Kinetics," Water Chlorination:
Environmental Impacts and Health Effects, Vol. 4, Jolley, R.l. et al., Eds.,
Ann Arbor Science, 297.
Hutton, P.H. and Chung, F.I. (1992a). "THM Formation Potential in
the Sacramento Delta: Part I", ASCE Journal of Water Resources Planning
and Management, accepted for publication January 1992.
Hutton, P.H. and Chung, F.I. (1992b). "THM Formation Potential in
the Sacramento Delta: Part II", ASCE Journal of Water Resources
Planning and Management, accepted for publication January 1992.
Koch, B., Krasner, S.W., Sclimenti, M.J. and Schimpff, W.K. (1991).
Predicting the Formation of DBPs by the Simulated Distribution System,
Journal AWWA, 83(10),62.
Pontius, F.W. (1991). "Disinfection - Disinfection By-Product Rule
Update", Journal AWWA, 83(12),24.
Reckhow, D.A. (1984). Organic Halide Formation and the Use of
Preozonation and Alum Coagulation to Control Organic Halide Precursors,
Doctoral dissertation, University of North Carolina, Chapel Hill.
Reckhow, D.A. and Edzwald, J.K. (1991). "Bromoform and Iodoform
Formation Potential Tests as Surrogates for THM Formation Potential",
Journal AWWA, 83(5),67.
Woodard, R.P. (1991). "Sources of Disinfection By-Product
Precursors," Proceedings from Protecting Drinking Water Quality at the
Source, California Water Resources Center Report No. 76,71.
Author: Paul Hutton
Back to Delta Modeling Section 1992 Annual Report Table of Contents
Last revised: 2001-10-01
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