Trihalomethane Formation Potential Modeling
[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. 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 (EPA) 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, the Department of Water Resources (DWR) has
been studying THM precursors in Delta waters for several years. More recently,
the Department has become active in modeling THM precursor fate and movement in
the Delta as well as modeling THM formation and speciation.
This chapter summarizes DWR's most recent efforts to mathematically model THM
formation potential in Delta waters. The first section presents a comparison
between DWR's model and the THM kinetic equations employed by the EPA-Malcolm
Pirnie (MPI) water treatment plant (WTP) model (Harrington et al. 1992). The
second section of this chapter summarizes work that was undertaken to
characterize THM speciation according to first order chemical kinetics. The
final section briefly discusses a current project to simulate
historically-observed THM precursor transport in the Delta.
A Comparison with EPA-MPI THM
At the request of the Municipal Water Quality Investigations committee, a
comparison of the modeling approaches developed by DWR (Hutton and Chung 1992a,
1992b, 1993a, 1993b) and EPA-MPI (Harrington et al. 1992) was undertaken. The
DWR approach was contrasted with EPA-MPI's THM kinetic equations, not with the
entire WTP model. Several aspects of the EPA-MPI THM equations were evaluated
both qualitatively and quantitatively. Sensitivity analyses show the EPA-MPI
kinetic equations tend to respond erroneously (in an incremental sense as well
as in an absolute sense) to changes in bromide concentration.
To provide an "apples-to-apples" comparison, the DWR model was
recalibrated with the University of Arizona database (Amy et al. 1987) to
generalize its applicability to varying reaction conditions. This database is
herein referred to as the UA database. Although the recalibrated DWR model is
similar to the EPA-MPI model in terms of fit to the UA database, the DWR model
responds in a more appropriate manner to incremental changes in bromide
concentration. Furthermore, the DWR model requires the calibration of only two
equations (14 model constants) to predict individual THM species concentrations,
compared with EPA-MPI requiring calibration of 6 equations (38 model constants).
Recognizing limitations associated with high chlorine doses used to develop
the UA database, the EPA-MPI and DWR models were recalibrated with a small data
set provided by the Metropolitan Water District (MWD). This exercise showed the
DWR formulation provides a superior fit to observed data and provides superior
sensitivity to incremental changes in bromide concentration. This exercise also
illustrated the potential difficulty of calibrating the EPA-MPI formulation to a
Based on the aforementioned comparison between THM models, the following
recommendations are offered:
1. An extensive database being developed by MWD should be used to calibrate
a THM submodel employing the bromine distribution factors, rather than relying
on the current EPA-MPI power function formulation.
2. It may be desirable to include different variables or otherwise improve
upon the proposed form of the bromine
incorporation factor (η). For example, Symons et al. (1993) shows that
the initial bromide to average free available chlorine molar ratio is an
important variable in predicting η. The DWR approach is not constrained
to predicting η directly, however. As
an alternative to predicting η directly, chloroform concentration could
be predicted, possibly in a manner similar to the current EPA-MPI methodology.
Then from the bromine distribution factor relationship s0 = [CHCl3]/[TTHM],
s0 could be estimated. And since s0 is functionally related to η, the
remaining THM species could be determined. This may be an attractive
alternative, particularly if differential rate equations can be developed for
chloroform and [TTHM].
3. The bromine distribution factor relationships have been validated for
delta waters treated under a variety of conditions. They have also been shown
to be valid for the waters and conditions incorporated in the UA database.
Nevertheless, these equations should be validated with additional data to test
their general applicability. Assuming the worst case in which the bromine
distribution factors have to be recalibrated for different waters, the
proposed formulation will require the calibration of six equations with 26
constants (which is still preferable to the EPA-MPI requirement of six
equations and 38 model constants).
4. For planning studies that focus on source water management impacts, it
may be desirable to agree upon a set (or sets) of "standard"
treatment conditions, e.g. simulated distribution system (SDS-THM) three-hour
or 24-hour reaction conditions. These conditions can then be substituted into
the THM submodel to develop a simplified form that varies only with influent
water quality conditions. This simplified set of equations can be used to
estimate THM formation from DWRDSM model output. This simplified analysis of
source water management impacts is referred to as a "Level I"
5. Similar to recommendation 4, for planning studies that focus on WTP
design and operational impacts, it may be desirable to agree upon a set (or
sets) of "standard" influent conditions, e.g., critical winter, dry
summer, or normal year. These conditions can then be employed as input to the
EPA-MPI WTP model. A simplified analysis of WTP design and operational impacts
is also referred to as a "Level I" analysis.
6. Finally, more refined planning studies (particulary those where THM
formation at a particular WTP is the main objective) may wish to consider source
water management and WTP design and operations as one system. For this type of
study, DWRDSM output can be used directly as input to the EPA-MPI WTP model.
This more sophisticated approach is referred to as a "Level II"
Critique of EPA-MPI THM
The EPA-MPI THM equations were evaluated both qualitatively and
quantitatively. The qualitative critique focused on model form, while the
quantitative critique focused on model sensitivity.
Questionable Functional Forms. Amy et al. (1987) emphasized the development
of "chemically rational yet statistically valid" models. Many aspects
of the EPA-MPI THM equations do not adhere to this philosophy:
1. The precursor-related parameter UVA*DOC was determined by Amy et al.
to be the best overall in terms of chemical significance and statistical
fit. According to the authors, "The chemical significance of this
parameter is that DOC represents a means of defining precursor
concentration while UV absorbance provides an indication of precursor
reactivity in forming THMs". The EPA-MPI equations for individual
THMs use a variety of precursor-related parameters: UVA*DOC, UVA/DOC, UVA,
and Br/DOC. This deviation from a single precursor-related parameter
appears to be a compromise of "chemical significance" for
statistical fit. The EPA-MPI equations (six equations and 38 model
constants) developed from the UA database are as follows:
2. The EPA-MPI model does not sum the four individual THM species
predictions to arrive at a total mass weight. Rather, the predictive
approach is to estimate total mass weight as the product of total molar
weight (Eq. 5) and apparent molecular weight (Eq. 6). This approach does not
constrain total THMs to equal the sum of the four species. The magnitude of
deviation associated with this approach has not been explored.
3. Eq. 6 does not take advantage of a priori knowledge of boundary
conditions, i.e. a minimum AMW of 119.4 μg/μmole at 100 percent
chloroform and a maximum AMW of 252.7 μg/μmole at 100 percent
bromoform. Disregarding these boundary conditions permits the
regression equation to predict infeasible values under extreme conditions.
4. Eqs. 1 through 4 do not approximate the nonlinear response of THM
formation to bromide over a wide range of bromide. Fig. 1 gives examples of
the response to bromide as observed by others. Harrington et al. (1991)
attemped to circumvent this problem by segregating data into bromide ranges
and modeling in a piece-wise fashion. While a piece-wise approach is
certainly valid, it can result in a discontinuity at the interface between
5. The resulting piece-wise equations show that while a given parameter may
be directly related to THM formation under one bromide range, the same parameter
may be inversely related to THM formation under another bromide range. This
behavior, while easily handled by the DWR model with the bromine distribution
factors, is not addressed by Eqs. 1 through 4.
Performing sensitivity analyses on the EPA-MPI individual THM equations
revealed erroneous model sensitivities, particularly with respect to bromide.
1. The base conditions employed for sensitivity analyses are adopted from
Chowdhury et al. (1991), a paper on the original development of the EPA-MPI
individual THM equations. Base conditions are: DOC = 3 mg/L, UVA = 0.045, pH =
7.5, Cl2 =4 mg/L, T = 25 ºC, and bromide takes on alternate values
of 0.03, 0.3 and 0.6 mg/L. An additional base condition set for this analysis
was t = 24 hrs.
2. See Figs. 2 and 3. While the CHCl3 sensitivity given by Eq. 1
appears to follow the general pattern shown in Fig. 1, the CHCl2Br
and CHClBr2 estimates from Eqs. 2 and 3 "blow up" with
increases in bromide. The CHBr3 estimates from Eq. 4 are relatively
insensitive to bromide increases.
3. The piece-wise approach constrains the model from "blowing up".
However, note the extreme discontinuities produced by this approach. The
piece-wise model results in CHBr3 being even less sensitive to
bromide increases and results in total THMs decreasing with increasing bromide,
an erroneous result. Fig. 4 shows TTHM as the sum of Eqs. 1 through 4, rather
than as the product of Eqs. 5 and 6.
Recalibration of DWR's Model
DWR's model was originally developed to predict THM formation under
pre-defined test conditions, first for THMFP and later for SDS-THM. In this
study, the model was reconfigured to predict individual THM compounds under
varying test conditions and was calibrated with the UA database. As with the
original formulation, individual species mass concentrations are calculated as
where [TTHM] is now predicted from Eq. 5 and s0, s1, s2
and s3 are the bromine distribution factors previously defined as:
It was unnecessary to recalibrate Eqs. 11 through 14 to the UA database. The
bromine incorporation factor (η) was modeled
with a form previously suggested:
where k is the bromine saturation level and takes on a value of 3. To predict
THM speciation under varying test conditions, β was expanded into a multivariable
The generalized bromine incorporation factor formulation shown in Eqs. 15 and
16 are preliminary and alternative formulations are being considered. Eq. 16 was
developed with a backward stepwise log-linear regression procedure using a copy
of the UA database provided by MPI. The database has 1,025 data points varying
somewhat from the 995 database reported by Amy et al. (1987). As a caveat on the
bromine incorporation factor, note that the EPA-MPI model implicitly uses the
concept of bromine incorporation factor through the AMW term. AMW is a linear
function of the bromine incorporation factor:
Comparison of the DWR Model
with the EPA-MPI Model
The previous discussion shows that the DWR model
requires the calibration of two equations, one for [TTHM] and one for β.
Model calibration of 14 constants is required, compared with the EPA-MPI
calibration requirements of 38 model constants.
Observed values from the UA database were compared with predictions from the
DWR model and the EPA-MPI model. Comparisons are shown in Figs. 5 through 7 as
relative frequency histograms of percent deviation, where:
||% Deviation = (Predicted - Observed) / Observed * 100
1. To allow for an unbiased comparison, the EPA-MPI model was also
recalibrated to the available UA database. Recalibration was necessary
because, while the equations for η and AMW
were based on 1025 observations (Harrington et al. 1992), Eqs. 1 through 5
were developed from only 995 observations. Recalibrated equations are as
Note that the Br+1 term was dropped from Eq. 23. Regression gave a negative
exponent for this term. The backward stepwise procedure indicated that this
term and several others were not statistically significant. Other terms were
not dropped from the equations for this analysis, however.
2. For CHClBr2 predictions, percent deviation is not displayed in Fig. 6
when bromide is less than 0.10 mg/L. Similarly for CHBr3, percent
deviation is not displayed in Fig. 7 when bromide is less than 0.25 mg/L.
These omissions are justified by observing that within these bromide ranges
the species concentrations tend to take on values much less than 1 μg/L.
3. Overall, both models are similar in their abilities (or lack thereof) to
match the UA database.
DWR model sensitivity to bromide is shown in Figs. 2 through 4. Unlike the
EPA-MPI model, DWR's model sensitivities correspond in a relative sense to
trends shown in Fig. 1.
While the DWR model is superior in its incremental response to bromide, it is
reasonable to assume that it does not adequately predict THM formation under
delta drinking water conditions because of UA database limitations sited by
Harrington et al. (1992). In an attempt to overcome this limitation, the DWR
model was recalibrated with a small database provided by MWD. This data
represents 60 observations of June 1992 conditions at Greene's Landing, West
Branch SWP water at Foothill, and East Branch SWP water at Devil Canyon.
1. The [TTHM] equation was recalibrated with a backward stepwise log-linear
regression procedure. The chlorine dose term was redefined as an
"available chlorine" dose by accounting for ammonia chlorine
demands. A bromide term was not included in the calibration because the data
set is biased in its distribution of bromide and precursors, i.e., Greene's
Landing has low bromide and low precursors while the other stations have high
bromide and high precursors. Inclusion of a chlorine residual term did not
appear to improve the regression:
2. The β equation was also recalibrated. Stepwise regression
eliminated terms for t, T, and pH. Again, the chlorine dose term accounts for
ammonia chlorine demand:
3. Bromine distribution factors (Eqs. 11 through 14) were not recalibrated.
The MPI-EPA THM equations were also recalibrated with the same data. Again, a
backward stepwise log-linear regression procedure was used. This procedure
eliminated a number of variables from the predictive equations, pointing out a
disadvantage of using an approach that requires more equations and calibration
constants. It is possible that these terms would not drop out if more data were
available for calibration.
Observed values were compared with predictions from the recalibrated DWR and
EPA-MPI models. The recalibrated DWR model gives superior predictions for TTHM
and all four compounds. The difference between models is most pronounced for
total THMs, where DWR estimates are within ±10 percent for 55 of the 60
observations and the EPA-MPI estimates are within ±10 percent for only 34 of
the 60 observations. Again, the DWR model shows good sensitivity to changes in
bromide while the EPA-MPI model does not.
THM Speciation with First-Order Kinetics
By assuming that bromine is not actively involved in the oxidation of
precursor material and is involved only in substitution reactions, THM
speciation was modeled as a consecutive irreversible three-stage reaction:
where k1, k2, and k3 are first order
reaction rate constants defined by the following differential equations:
The following bromine distribution factor relationships result after solving
this system of differential equations and assuming that the initial chloroform
concentration is equal to [TTHM]:
From Eq. 30, a value for the rate constant k1 may be estimated by
plotting ln(1/s0) versus η and
determining a best-fit slope. This technique results in an estimate of k1=1.19
for the calibration data. Rate constant k2 may be estimated by
setting Eq. 27 equal to zero, dividing through by [TTHM], substituting in k1=1.19,
and determining values of s0(η) and
s1(η) for the value of
η such that s1 is maximized. This step can be satisfied
by visual inspection of the data, resulting in s0=0.334 and s1=0.340
at η=1.05 and:
In a similar manner, k3 may be estimated by setting Eq. 28 equal
to zero, dividing through by [TTHM], substituting in k2=1.17, and
determining values of s1(η) and s2(η)
for the value of η such that s2 is maximized. Values of s1=0.218
and s2=0.411 were estimated for η=1.90
The first order kinetic representation of the bromine distribution factors
can be summarized by substituting values for the rate constants into Eqs. 30
While these relationships provide some correspondence between observed and
predicted values, the correspondence is inferior to that provided by
probability-based polynomial relationships (Hutton
and Chung 1993b). Deviation between observed and predicted values, particularly
at high values of η, may suggest that bromine substitution reactions do not
always follow first order kinetics.
Simulation of Delta THM Precursors
The purpose of this project is to validate DWRDSM's use as a
tool to track bromide and THM precursors in the delta. DWR is currently running
a 24-month DWRDSM simulation (12-month model "warm-up") of historic
conditions from October 1989 through September 1991, tracking bromide, dissolved
organic carbon (DOC), ultraviolet absorbance at 254 nm (UVA), and THMFP as
carbon (TFPC). The simulation employs a monthly time step, a 19-year mean tide,
and DAYFLOW hydrology. When available, water quality boundary conditions are
based on historic grab-sample bromide and precursor data collected by DWR (Input
1993). It is anticipated that results of this historic simulation will be
presented at the American Society of Civil Engineers Hydraulics Division's 1993
National Conference in San Francisco (Hutton and Enright 1993).
Amy, G.L., Chadik, Z.K. and Chowdhury, Z.K. (1987). "Developing
Models for Predicting Trihalomethane Formation Potential and Kinetics."
Journal AWWA, 79(7), 89-97.
Chowdhury, Z.K., Amy, G.L. and Siddiqui, M. (1991). "Modeling
Effects of Bromide Ion Concentrations on the Formation of Brominated
Trihalomethanes." Water Research for the New Decade, Proceedings 1991
AWWA Annual Conference, Philadelphia, PA, 313-322.
Harrington, G.W., Chowdhury, Z.K. and Owen, D.M. (1991). "A Computer
Model to Simulate Organics Removal and Trihalomethane Formation." Water
Quality for the New Decade, Proceedings 1991 AWWA Annual Conference,
Philadelphia, PA, 589-624.
Harrington, G.W., Chowdhury, Z.K. and Owen, D.M. (1992). "Developing
a Computer Model to Simulate DBP Formation During Water Treatment."
Journal AWWA, 84(11), 78-87.
Hutton, P.H. and Chung, F.I. (1992a). "Simulating THM Formation
Potential in the Sacramento Delta: Part I." Journal of Water Resources
Planning and Management, ASCE, 118(5), 513-529.
Hutton, P.H. and Chung, F.I. (1992b). "Simulating THM Formation
Potential in the Sacramento Delta: Part II." Journal of Water Resources
Planning and Management, ASCE, 118(5), 530-542.
Hutton, P.H. and Chung, F.I. (1993a). "Correlating Trihalomethane
Data." accepted for publication to Journal of Environmental
Engineering, February 1993.
Hutton, P.H. and Chung, F.I. (1993b). "Bromine Distribution Factors
in THM Formation." accepted for publication to Journal of Water
Resources Planning and Management, March 1993.
Hutton, P.H. and Enright, C. (1993). "Simulating THM Precursors
Transport with DWRDSM." Proceedings 1993 ASCE Annual Hydraulics
Conference, San Francisco, CA, 6 pp., in press.
Input Data for Historic Simulation Model Run of THM Precursors in Delta.
(1993). letter from Marvin Jung and Associates, February 1, 6 pp.
Lange, A.L., and Kawczynski, E. (1978). "Controlling Organics: The
Contra Costa County Water District Experience." Journal AWWA, 70(11),
Pourmoghaddas, H., Stevens, A.A., Kinman, R.N., Dressman, R.C., Moore,
L.A., and Ireland, J.C. (1993). "Effect of Brimide Ion on Formation of
HAAs During Chlorination." Journal AWWA, 85(1), 82-87.
Symons, J.M., Krasner, S.W., Simms, L.A., and M. Sclimenti (1993).
"Measurement of THM and Precursor Concentrations Revisited: The Effect of
Bromide Ion." Journal AWWA, 85(1), 51-62.
Author: Paul Hutton
Back to Delta Modeling Section 1993 Annual Report Table of Contents
Last revised: 2001-11-15
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