Skip Links

USGS - science for a changing world

Scientific Investigations Report 2011–5136

Prepared in cooperation with the Massachusetts Department of Environmental Protection

Determination of Dilution Factors for Discharge of Aluminum-Containing Wastes by Public Water-Supply Treatment Facilities into Lakes and Reservoirs in Massachusetts

By John A. Colman, Andrew J. Massey, and Sara B. Levin

Right-click to download or Save As (5.65 MB)


Dilution of aluminum discharged to reservoirs in filter-backwash effluents at water-treatment facilities in Massachusetts was investigated by a field study and computer simulation. Determination of dilution is needed so that permits for discharge ensure compliance with water-quality standards for aquatic life. The U.S. Environmental Protection Agency chronic standard for aluminum, 87 micrograms per liter (µg/L), rather than the acute standard, 750 µg/L, was used in this investigation because the time scales of chronic exposure (days) more nearly match rates of change in reservoir concentrations than do the time scales of acute exposure (hours).

Whereas dilution factors are routinely computed for effluents discharged to streams solely on the basis of flow of the effluent and flow of the receiving stream, dilution determination for effluents discharged to reservoirs is more complex because (1), compared to streams, additional water is available for dilution in reservoirs during low flows as a result of reservoir flushing and storage during higher flows, and (2) aluminum removal in reservoirs occurs by aluminum sedimentation during the residence time of water in the reservoir. Possible resuspension of settled aluminum was not considered in this investigation. An additional concern for setting discharge standards is the substantial concentration of aluminum that can be naturally present in ambient surface waters, usually in association with dissolved organic carbon (DOC), which can bind aluminum and keep it in solution.

A method for dilution determination was developed using a mass-balance equation for aluminum and considering sources of aluminum from groundwater, surface water, and filter-backwash effluents and losses caused by sedimentation, water withdrawal, and spill discharge from the reservoir. The method was applied to 13 reservoirs. Data on aluminum and DOC concentrations in reservoirs and influent water were collected during the fall of 2009. Complete reservoir volume was determined to be available for mixing on the basis of vertical and horizontal aluminum-concentration profiling. Losses caused by settling of aluminum were assumed to be proportional to aluminum concentration and reservoir area. The constant of proportionality, as a function of DOC concentration, was established by simulations in each of five reservoirs that differed in DOC concentration.

In addition to computing dilution factors, the project determined dilution factors that would be protective with the same statistical basis (frequency of exceedance of the chronic standard) as dilutions computed for streams at the 7-day-average 10-year-recurrence annual low flow (the 7Q10). Low-flow dilutions are used for permitting so that receiving waters are protected even at the worst-case flow levels. The low-flow dilution factors that give the same statistical protection are the lowest annual 7-day-average dilution factors with a recurrence of 10 years, termed 7DF10s. Determination of 7DF10 values for reservoirs required that long periods of record be simulated so that dilution statistics could be determined. Dilution statistics were simulated for 13 reservoirs from 1960 to 2004 using U.S. Geological Survey Firm-Yield Estimator software to model reservoir inputs and outputs and present-day values of filter-effluent discharge and aluminum concentration.

Computed settling velocities ranged from 0 centimeters per day (cm/d) at DOC concentrations of 15.5 milligrams per liter (mg/L) to 21.5 cm/d at DOC concentrations of 2.7 mg/L. The 7DF10 values were a function of aluminum effluent discharged. At current (2009) effluent discharge rates, the 7DF10 values varied from 1.8 to 115 among the 13 reservoirs. In most cases, the present-day (2009) discharge resulted in receiving water concentrations that did not exceed the standard at the 7DF10. Exceptions were one reservoir with a very small area and three reservoirs with high concentrations of DOC. Maximum permissible discharges were determined for water-treatment plants by adjusting discharges upward in simulations until the 7DF10 resulted in reservoir concentrations that just met the standard. In terms of aluminum flux, these discharges ranged from 0 to 28 kilograms of aluminum per day.

First posted September 16, 2011

Revised December 30, 2016

For additional information contact:
U.S. Geological Survey
Massachusetts-Rhode Island Water Science Center
U.S. Geological Survey
10 Bearfoot Road
Northborough, MA 01532
(508) 490-5000

Part or all of this report is presented in Portable Document Format (PDF); the latest version of Adobe Reader or similar software is required to view it. Download the latest version of Adobe Reader, free of charge.

Suggested citation:

Colman, J.A., Massey, A.J., and Levin, S.B., 2011, Determination of dilution factors for discharge of aluminum-containing wastes by public water-supply treatment facilities into lakes and reservoirs in Massachusetts (ver. 1.1, December 2016): U.S. Geological Survey Scientific Investigations Report 2011–5136, 36 p., available only at




Purpose and Scope

Previous Investigations

The Dilution-Factor Method

Calculating Dilution

Calculating the Settling Velocity

Dilution at Low Flow

Data Requirements

Flows and Reservoir Volumes

Filter-Backwash Effluent Flows

Water Quality

Application of the Dilution-Factor Method to Reservoirs

Reservoirs Studied

Flow, Area, and Volume Calculations

Water-Sample Collection, Processing, and Chemical Analysis

Quality Assurance of the Water-Quality Data

Water-Quality Results and Associations

Aluminum Mixing in Reservoirs

Settling-Velocity Results

Aluminum Simulation Results

Dilution-Factor Results

Low-Flow Dilution

Finding the Maximum Permissible Aluminum Discharge

Discussion of Method Applications

Permitted Discharges

Limits to the Applicability of the Method

Environmental Consequences of Aluminum Discharges


References Cited

Appendix 1. Method for solving for aluminum concentrations in reservoirs using the MatLab differential equation solver

Appendix 2. Massachusetts water-supply reservoirs not included in the application of dilution factors

Appendix 3. Bathymetry- and flow-data sources for 13 Massachusetts drinking-water supply reservoirs

Appendix 4. Water-quality data from 13 Massachusetts reservoirs, influent streams, filter-backwash effluents containing aluminum, and streams sampled during August–November 2009

Accessibility FOIA Privacy Policies and Notices logo U.S. Department of the Interior | U.S. Geological Survey
Page Contact Information: Contact USGS
Page Last Modified: Wednesday, January 04, 2017, 01:53:30 PM