PDM4 MODELING OF DIDECYL DIMETHYL AMMONIUM CHLORIDE (DDAC) IN
ONCE-THROUGH

INDUSTRIAL WATER SYSTEMS

David C. Bays, Microbiologist

Kathryn V. Montague, Biologist

Rick Petrie, Team Leader

Risk Assessment and Science Support Branch

Antimicrobials Division

Office of Pesticide Programs

U.S. EPA

INTRODUCTION

	

This document provides estimated environmental concentrations (EECs) in
the receiving body of water from the use of didecyl dimethyl ammonium
chloride (DDAC) in industrial cooling water systems.  DDAC has been
shown to be hydrolytically stable under abiotic and buffered conditions.
 Metabolic transformation is unlikely to occur; therefore, degradation
products of DDAC are not expected.  The Probabilistic Distribution Model
version 4 (PDM4) was used to evaluate the DDAC concentration in stream
water resulting from the use of DDAC products in once-through cooling
water systems.  An average sized plant was modeled as being located on
small, average, and large rivers.  The chances of exceedance on any
given day were determined, as well as percent chances of exceedance over
extended durations. 

Overview of PDM4

PDM4 calculates downstream chemical concentrations from a chemical
discharge using the probabilistic distribution model.  The algorithm
used is taken from DiToro (1984).  A simple mass balance approach forms
the basis of PDM.  However, the input variables are not single point
estimates, because, in reality, these variables are not constant. 
Streams follow a highly variable seasonal flow pattern and numerous
variables in a manufacturing process can affect the chemical
concentration and flow rate of the effluent. PDM4 models the stream flow
as constantly changing and calculates the probability that the
concentration in a given target stream will exceed some target value.
Specifically, it calculates the percent of days per year that the
concentration of concern is exceeded.  PDM4 uses probability
distributions as inputs and calculates the resulting probability
distribution of the concentration in the stream. 

ONCE-THROUGH COOLING WATER

Inputs

Application Rate  tc "Application Rate " \l 3 

  	The dose rates for DDAC from product labels ranged from 32 to 63 ppm
a.i. (i.e., 1 part DDAC per million parts of water flowing through the
system) for continuous feed and from 1000 to1800 ppm a.i. for
intermittent treatment.  For this assessment, four rates were modeled:
32 ppm a.i. (low dose – continuous feed), 63 ppm a.i. (high dose –
continuous feed), 1000 ppm a.i. (low dose – intermittent treatment)
and 1800 ppm a.i. (high dose – intermittent treatment). 

Power Plant Information  tc "Power Plant Information " \l 3 

In modeling the fate of DDAC in the receiving body of water, it was
assumed that the 7Q10 flow rate (a flow rate that, once every ten years,
a stream is expected to be below for seven consecutive days) was assumed
to be the normal cooling water flow rate.  This value was chosen because
it is assumed that electric plants would need to have a steady supply of
cooling water, and the 7Q10 flow reflects a rate that could be
maintained continuously by the power plant.  This is not a conservative
assumption, since electric plants may use more cooling water under
normal conditions, though at a greater risk of running out of usable
water.  For lack of better data, however, these values were used.

PDM4 Model Inputs  tc "PDM4 Model Inputs " \l 3 

A summary of the input parameters is described below.  

Release Days - It has been assumed that the product is released 365 days
per year.

Pretreatment Release – The following equations were used to calculate
the loading (kg/site/day):

Continuous Feed Scenario-Calculation for Loading (kg/site/day):

System Flow (MLD) * 106 (Conversion factor for million liters/day to
liters/day) 	(Equation #1)

* 1 (kg water/liter of water) * dose rate (kg/kg) 	

where,					

Dose rate (kg of chemical/ kg of water) = dose rate (ppm) * 10-6  		
(Equation #2)

The cooling system flow rate was assumed to be identical to the 7Q10
flow rate (a flow rate that, once every ten years, a stream is expected
to be below for seven consecutive days).

 

Intermittent Feed Scenario-Calculation for Loading (kg/site/day): As no
information was provided regarding the application time associated with
intermittent treatment, it was assumed that one application is made per
day for 15 minutes:

System Flow (MLD) * 106 (Conversion factor for million liters/day to
liters/day)  	(Equation #3)

* 1 (kg water/liter of water) * dose rate (kg/kg) * (0.25/24 (hrs/day)) 

					

where, 

 

Dose rate (kg of chemical/ kg of water) = dose rate (ppm) * 10-6 		
(Equation #4)

Concentration of Concern - PDM4 is designed to report the number of days
that the concentration in the water body exceeds a concentration of
concern that has been specified by the user.  For this study, the model
was run multiple times using different COCs to determine a curve.  The
COCs considered for each flow regime are as follows: 14, 18, 69, 73, 95,
320, 1000 ppb a.i.  These COC values were derived from studies of the
sensitivity of various species to DDAC.

The input parameters are summarized in Table 1 below.

Table 1.  PDM4 Model Inputs

Parameter	Value	Rationale

Industry Type	Steam Electric Power Plants (SIC #4911)

Various NPDES	EPA assumption as being the representative facility for
once-through industrial water systems using DDAC.

Release Days	365	EPA assumption.

Pretreatment Release	Determined for each site using Eq. 1-4	See
discussion regarding Eq. 1-4.

Concentration of Concern	14, 18, 69, 73, 95, 320, 1000 ppb a.i	A range
was used to determine a curve.  The range is based on the sensitivity of
different species to DDAC.



The three different flow regimes consisted of power plants with stream
flow rates of 100 ± 10 MGD (million gallons per day), 500 ± 50 MGD,
and 1000 ± 50 MGD.  The low, medium, and high stream flow rates
correspond to 378.5 ± 37.85, 1982.5 ± 189.25, and 3785 ± 189.25
million liters per day.  These plants were pulled from a database of
NPDES plant codes based on the above criterion.  Tables 2, 3, and 4
below show details regarding the power plants and their cooling streams.


 

Table 2.  Low Flow (100 MGD1) Stream Specifications

NPDES	Mean Stream

Flow (MLD2)	Mean7Q103

Stream Flow (MLD)

IA0033235	401	2.84

PA0002062	391	4.09

LA0003042	384	44.6

MI0038172	379	14.0

OK0002682	363	3.37

WV0005525	359	14.6

IL0036919	356	3.89

LA0036145	354	13.6

UT0000116	352	32.4

TX0054500	352	26.8

PA0008443	337	12.6

IL0048321	336	97.0

1.	MGD = million gallons per day

2.	MLD = million liters per day 

3.	Mean 7Q10 = Seven consecutive days of lowest stream flows over a ten
year period 

	

Table 3.  Medium Flow (500 MGD1) Stream Specifications

NPDES	Mean Stream

Flow (MLD2)	Mean7Q103

Stream Flow (MLD)

MA0004367	2,030	227

IA0000108	1,970	61.3

NM0000108	1,970	5.92

FL0025526	1,960	653

IN0032948	1,950	153

TX0001163	1,870	11.4

OH0010421	1,840	59.8

IN0041246	1,820	167

PA0002054	1,790	115

MN0000906	1,750	28.9

NH0001431	1,730	75.7

IN0038806	1,720	58.2

1.	MGD = million gallons per day

2.	MLD = million liters per day 

3.	Mean 7Q10 = Seven consecutive days of lowest stream flows over a ten
year period 

Table 4.  High Flow (1000 MGD1) Stream Specifications

NPDES	Mean Stream

Flow (MLD2)	Mean7Q103

Stream Flow (MLD)

GA0004341	3,960	838

WA0003280	3,830	592

KS0079057	3,760	20.4

NC0005088	3,690	812

SC0001104	3,650	50.3

IL0002186	3,640	1,170

1.	MGD = million gallons per day

2.	MLD = million liters per day 

3.	Mean 7Q10 = Seven consecutive days of lowest stream flows over a ten
year period 

	Twelve different sites throughout the United States were tested in the
model from the low and medium stream regimes, and six were tested from
the high flow regime.

RESULTS

	For each reach, PDM4 calculates the percent of days per year that a
reach would have concentrations above a particular COC.  These values
were averaged by Versar within each of the three different flow regimes
(i.e., low, medium, and high), giving average percentages of exceedance.
Versar also looked at the worst-case scenarios for the low, medium, and
high stream flows considered.  These calculations were performed for
four dose rates: intermittent low- and high-end doses, and the
continuous low- and high-end doses.  Versar also calculated the chance
of exceeding a particular COC over time periods of 48 hours (2 days) and
96 hours (4 days).  Average results for each of the three flow regimes
are presented in Tables 5, 6, and 7.

Table 5.  Average Percent of Days per Year COC Exceeded

(Dose = 32 ppm a.i.-Continuous Low-End Dose)

COC1 (ppb)	LF2 Percent Days COC Exceeded (%)	LF-Standard

Deviation (%)	MF3-Percent Days COC Exceeded

(%)	MF-Standard Deviation (%)	HF4-Percent Days COC Exceeded

(%)	HF-Standard

Deviation (%)

14	96.4	9.59	99.4	1.34	100	0.0744

18	94.6	13.4	99.2	1.95	99.9	0.177

69	80.1	32.8	94.9	10.3	95.9	7.82

73	79.4	33.4	94.6	10.9	95.5	8.69

95	76.3	35.9	92.9	14.1	93	13.4

320	62.7	40.4	81.2	27.1	80	35.7

1000	47	37.7	63.3	27.9	70.6	41.6

1. COC = Concentration of Concern

2. LF = Low Flow Regime (100 MGD) 

3. MF = Medium Flow Regime (500 MGD)

4. HF = High Flow Regime (1000 MGD)

Table 6.  Average Percent of Days per Year COC Exceeded

(Dose = 63 ppm a.i.- Continuous High-End Dose)

COC1 (ppb)	LF2 Percent Days COC Exceeded (%)	LF-Standard

Deviation (%)	MF3-Percent Days COC Exceeded

(%)	MF-Standard Deviation (%)	HF4-Percent Days COC Exceeded

(%)	HF-Standard

Deviation (%)

14	99.1	2.59	99.8	0.439	100	0.00802

18	98.4	4.53	99.7	0.671	100	0.0184

69	88.2	24.1	97.8	4.72	99.1	1.55

73	87.6	25	97.6	5.05	99	1.82

95	84.5	28.6	96.7	6.91	98.1	3.62

320	70.2	39.3	88.3	21.1	87	24.7

1000	56.9	39.9	75.2	28.5	76.2	39.4

1. COC = Concentration of Concern

2. LF = Low Flow Regime (100 MGD) 

3. MF = Medium Flow Regime (500 MGD)

4. HF = High Flow Regime (1000 MGD)



Table 7.  Average Percent of Days per Year COC Exceeded 

(Dose = 1000 ppm a.i.-Intermittent Low-End Dose)

COC1 (ppb)	LF2 Percent Days COC Exceeded (%)	LF-Standard

Deviation (%)	MF3-Percent Days COC Exceeded

(%)	MF-Standard Deviation (%)	HF4-Percent Days COC Exceeded

(%)	HF-Standard

Deviation (%)

14	85.8	27.1	97.1	6.04	98.5	2.71

18	82.8	30.3	96.1	8.08	97.4	4.96

69	67.4	40.1	85.7	24	84	29.8

73	66.7	40.2	85.1	24.5	83.4	30.8

95	63.8	40.5	82.3	26.6	80.8	34.7

320	47.2	37.7	63.7	28	70.8	41.5

1000	28.2	29.3	37.4	24.5	54.3	37.6

1. COC = Concentration of Concern

2. LF = Low Flow Regime (100 MGD) 

3. MF = Medium Flow Regime (500 MGD)

4. HF = High Flow Regime (1000 MGD)

Table 8.  Average Percent of Days per Year COC Exceeded 

(Dose = 1800 ppm a.i.-Intermittent High-End Dose)

COC1 (ppb)	LF2 Percent Days COC Exceeded (%)	LF-Standard

Deviation (%)	MF3-Percent Days COC Exceeded

(%)	MF-Standard Deviation (%)	HF4-Percent Days COC Exceeded

(%)	HF-Standard

Deviation (%)

14	92.2	18	98.7	2.89	99.7	0.469

18	89.6	22.1	98.2	4.01	99.4	1.05

69	73.8	37.5	91.2	17	90.7	17.8

73	73.2	37.9	90.7	17.7	90.1	19

95	70.3	39.3	88.4	21.1	87	24.6

320	55.9	39.8	74.1	28.6	75.7	39.8

1000	38.2	34.4	51.4	26.6	64.4	41.2

1. COC = Concentration of Concern

2. LF = Low Flow Regime (100 MGD) 

3. MF = Medium Flow Regime (500 MGD)

4. HF = High Flow Regime (1000 MGD)

Tables 9, 10, 11, and 12 list the calculations for those power plants
with the highest exceedance rates for each of the three stream flow
sizes considered.

Table 9. Worst Case Scenarios: Percent of Days per Year COC Exceeded

(Dose = 32 ppm a.i.-Continuous Low-End Dose)

COC1 (ppb)	LF2-Percent Days COC Exceeded (%)	MF3-Percent Days COC
Exceeded

(%)	HF4-Percent Days COC Exceeded

(%)

14	100	100	100

18	100	100	100

69	100	100	100

73	100	100	100

95	100	100	100

320	100	100	100

1000	98.8	99.2	99.6

1. COC = Concentration of Concern

2. LF = Low Flow Regime (100 MGD)

3. MF = Medium Flow Regime (500 MGD)

4. HF = High Flow Regime (1000 MGD)

Table 10. Worst Case Scenarios: Percent of Days per Year COC Exceeded

(Dose = 63 ppm a.i.- Continuous High-End Dose)

COC1 (ppb)	LF2-Percent Days COC Exceeded (%)	MF3-Percent Days COC
Exceeded

(%)	HF4-Percent Days COC Exceeded

(%)

14	100	100	100

18	100	100	100

69	100	100	100

73	100	100	100

95	100	100	100

320	100	100	100

1000	99.9	99.9	100

1. COC = Concentration of Concern

2. LF = Low Flow Regime (100 MGD)

3. MF = Medium Flow Regime (500 MGD)

4. HF = High Flow Regime (1000 MGD)



Table 11. Worst Case Scenarios: Percent of Days per Year COC Exceeded

 (Dose = 1000 ppm a.i.-Intermittent Low-End Dose)

COC1 (ppb)	LF2-Percent Days COC Exceeded (%)	MF3-Percent Days COC
Exceeded

(%)	HF4-Percent Days COC Exceeded

(%)

14	100	100	100

18	100	100	100

69	100	100	100

73	100	100	100

95	100	100	100

320	98.8	99.2	99.6

1000	84.8	88.5	88.6

1. COC = Concentration of Concern

2. LF = Low Flow Regime (100 MGD)

3. MF = Medium Flow Regime (500 MGD)

4. HF = High Flow Regime (1000 MGD)

Table 12. Worst Case Scenarios: Percent of Days per Year COC Exceeded 

(Dose = 1800 ppm a.i.-Intermittent High-End Dose)

COC1 (ppb)	LF2-Percent Days COC Exceeded (%)	MF3-Percent Days COC
Exceeded

(%)	HF4-Percent Days COC Exceeded

(%)

14	100	100	100

18	100	100	100

69	100	100	100

73	100	100	100

95	100	100	100

320	99.8	99.9	100

1000	95.2	96.7	97.5

1. COC = Concentration of Concern

2. LF = Low Flow Regime (100 MGD)

3. MF = Medium Flow Regime (500 MGD)

4. HF = High Flow Regime (1000 MGD)



Tables 13, 14, 15, and 16 show the average of all power plants modeled,
and compares these values to the average of the three worst-case
scenarios that were presented in Tables 9, 10, 11, and 12, respectively.

Table 13.  Total Average Exceedance Rates vs. Worst-Case Exceedance
Rates 

(Dose = 32 ppm a.i.-Continuous Low-End Dose)

COC1 (ppb)	Percent of Days COC Exceeded (%)

	Total Average	Average of the Three Worst Case Scenarios (Table 9)

14	98.3	100

18	97.5	100

69	89.2	100

73	88.7	100

95	86.3	100

320	73.6	100

1000	58.2	99.2

1. COC = Concentration of Concern

Table 14.  Total Average Exceedance Rates vs. Worst-Case Exceedance
Rates

(Dose = 63 ppm a.i.-Continuous High-End Dose)

COC1 (ppb)	Percent of Days COC Exceeded (%)

	Total Average	Average of the Three Worst Case Scenarios (Table 10)

14	99.6	100

18	99.3	100

69	94.2	100

73	93.9	100

95	92.1	100

320	80.8	100

1000	68.1	99.9

1. COC = Concentration of Concern



Table 15.  Total Average Exceedance Rates vs. Worst-Case Exceedance
Rates

(Dose = 1000 ppm a.i.-Intermittent Low-End Dose)

COC1 (ppb)	Percent of Days COC Exceeded (%)

	Total Average	Average of the Three Worst Case Scenarios (Table 11)

14	92.9	100

18	91	100

69	78	100

73	77.4	100

95	74.6	100

320	58.5	99.2

1000	37.1	87.3

1. COC = Concentration of Concern

Table 16.  Total Average Exceedance Rates vs. Worst-Case Exceedance
Rates

(Dose = 1800 ppm a.i.-Intermittent High-End Dose)

COC1 (ppb)	Percent of Days COC Exceeded (%)

	Total Average	Average of the Three Worst Case Scenarios (Table 12)

14	96.3	100

18	95	100

69	84.1	100

73	83.6	100

95	80.9	100

320	67.1	99.9

1000	48.7	96.5

1. COC = Concentration of Concern

 tc " " \l 2 To calculate the chance of exceedance of a concentration of
concern over a consecutive number of days, the following assumptions
were made: 

The chance of exceedance on any given day at a site is independent of
whether exceedance occurred on previous days. 

Although the percentages calculated by PDM express the chance of
exceedance during at least part of a day, it is assumed for this
calculation that the percentages calculated by PDM imply exceedance over
the total day. 

 ADVANCE \d 4 	Based on these assumptions, the following formula can be
used to express the probability of exceedance over N consecutive days: 

 ADVANCE \d 4 

% probability = (Average Probability of Exceedance per Day/100%)N * 100%

Tables 17, 18, 19, and 20 show the calculation for these probabilities. 
These tables can be used to determine an appropriate COC, based on the
level of risk that is deemed acceptable.  The choice will depend on how
conservative a value is deemed necessary.

Table 17.  Percent Probability of Exceedance Over Consecutive Days

(Dose = 32 ppm a.i.-Continuous Low-End Dose)

COC1 (ppb)	Number of Consecutive Days

	Low Flow (100 MGD2)	Mid Flow (500 MGD2)	High Flow (1000 MGD2)

	2 day	4 day	2 day	4 day	2 day	4 day

14	92.9	86.4	98.8	97.6	100	100

18	89.5	80.1	98.4	96.8	99.8	99.6

69	64.2	41.2	90.1	81.1	92	84.6

73	63	39.7	89.5	80.1	91.2	83.2

95	58.2	33.9	86.3	74.5	86.5	74.8

320	39.3	15.5	65.9	43.5	64	41

1000	22.1	4.88	40.1	16.1	49.8	24.8

1. COC = Concentration of Concern

2. MGD = million gallons per day

Table 18.  Percent Probability of Exceedance Over Consecutive Days

(Dose = 63 ppm a.i.-Continuous High-End Dose)

COC1 (ppb)	Number of Consecutive Days

	Low Flow (100 MGD2)	Mid Flow (500 MGD2)	High Flow (1000 MGD2)

	2 day	4 day	2 day	4 day	2 day	4 day

14	98.2	96.4	99.6	99.2	100	100

18	96.8	93.8	99.4	98.8	100	100

69	77.8	60.5	95.6	91.5	98.2	96.4

73	76.7	58.9	95.3	90.7	98	96.1

95	71.4	51	93.5	87.4	96.2	92.6

320	49.3	24.3	78	60.8	75.7	57.3

1000	32.4	10.5	56.6	32	58.1	33.7

1. COC = Concentration of Concern

2. MGD = million gallons per day

Table 19.  Percent Probability of Exceedance Over Consecutive Days

(Dose = 1000 ppm a.i.-Intermittent Low-End Dose)

COC1 (ppb)	Number of Consecutive Days

	Low Flow (100 MGD2)	Mid Flow (500 MGD2)	High Flow (1000 MGD2)

	2 day	4 day	2 day	4 day	2 day	4 day

14	73.6	54.2	94.3	88.9	97	94.1

18	68.6	47	92.4	85.3	94.9	90

69	45.4	20.6	73.4	53.9	70.6	49.8

73	44.5	19.8	72.4	52.4	69.6	48.4

95	40.7	16.6	67.7	45.9	65.3	42.6

320	22.3	4.96	40.6	16.5	50.1	25.1

1000	7.95	0.632	14	1.96	29.5	8.69

1. COC = Concentration of Concern

2. MGD = million gallons per day

Table 20.  Percent Probability of Exceedance Over Consecutive Days

(Dose = 1800 ppm a.i.-Intermittent High-End Dose)

COC1 (ppb)	Number of Consecutive Days

	Low Flow (100 MGD2)	Mid Flow (500 MGD2)	High Flow (1000 MGD2)

	2 day	4 day	2 day	4 day	2 day	4 day

14	85	72.3	97.4	94.9	99.4	98.8

18	80.3	64.5	96.4	93	98.8	97.6

69	54.5	29.7	83.2	69.2	82.3	67.7

73	53.6	28.7	82.3	67.7	81.2	65.9

95	49.4	24.4	78.1	61.1	75.7	57.3

320	31.2	9.76	54.9	30.1	57.3	32.8

1000	14.6	2.13	26.4	6.98	41.5	17.2

1. COC = Concentration of Concern

2. MGD = million gallons per day

UNCERTAINTIES/LIMITATIONS

The following limitations apply to the results of this model:

The PDM4 database contains data on steam electric power plants in the
United States.  In the database, no differentiation was made between
those power plants that used a recirculating cooling water system and
those that did not.  In the absence of better data, it was assumed that
all power plants in the database used a once-through cooling water
system, and that the amount of cooling water used in normal conditions
was equal to the 7Q10 flow.  These assumptions may not be conservative.

It is possible in all cases that more than one facility is located on a
given reach.  For the purposes of modeling, however, it is assumed that
only one facility is located at each reach.

PDM4 is a screening-level model.  Screening-level models are rarely if
ever used as the sole justification for regulatory decision-making at
EPA.  Additional data and more rigorous tools are used to improve the
estimates of exposures and risks for such decisions.  Results may not
accurately reflect all of the information and data used by EPA to make a
regulatory decision on a chemical.

It has been assumed that a maintenance dose of the chemical is required
daily, and that intermittent doses are applied for 15 minutes a day.  

REFERENCES

Cloete TE, Smith Z, Saayman G.  1999. A Cooling Water System as a
Biofilm Reactor for the Treatment of Municipal Wastewater.  Water SA
Vol. 25 No. 3 July 1999.  Available on website   GOTOBUTTON BM_1_
http://www.wrc.org.za. 

DiToro, D. M.  1984.  Probability Model of Stream Quality Due to Runoff.
 ASCE.  Journal of Environmental Engineering.  110(3):607-628.

EFAST Help, beta version, 2004.

Genest, Dan, Dominion Power. Telephone interview.  June 14, 2004.

Versar, 2005.  Memorandum. Draft Environmental Fate Science Chapter for
DDAC RED.  From Adria Diaz and Patricia Wood, Versar, Inc. to Srinivas
Gowda, USEPA. Date: August 30, 2005.  



Appendix: Input/Output Files

  PAGE  1 

