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Response Curves for Phosphorus Plume Lengths from Reactive-Solute-Transport Simulations of Onland Disposal of Wastewater in Noncarbonate Sand and Gravel Aquifers

By John A. Colman

Prepared in cooperation with the Massachusetts Department of Environmental Protection

Scientific Investigations Report 2004-5299


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The citation for this report, in USGS format, is as follows:

Colman, J.A., 2005, Response curves for phosphorus plume lengths from reactive-solute-transport simulations of onland disposal of wastewater in noncarbonate sand and gravel aquifers: U.S. Geological Survey Scientific Investigations Report 2004-5299, 28 p.

 For more information about USGS activities in Massachusetts and Rhode Island, visit the USGS MA-RI Water Science Center Home Page.


Surface-water resources in Massachusetts often are affected by eutrophication, excessive plant growth, which has resulted in impaired use for a majority of the freshwater ponds and lakes and a substantial number of river-miles in the State. Because supply of phosphorus usually is limiting to plant growth in freshwater systems, control of phosphorus input to surface waters is critical to solving the impairment problem. Wastewater is a substantial source of phosphorus for surface water, and removal of phosphorus before disposal may be necessary. Wastewater disposed onland by infiltration loses phosphorus from the dissolved phase during transport through the subsurface and may be an effective disposal method; quantification of the phosphorus loss can be simulated to determine disposal feasibility. In 2003, the U.S. Geological Survey, in cooperation with the Massachusetts Department of Environmental Protection, initiated a project to simulate distance of phosphorus transport in the subsurface for plausible conditions of onland wastewater disposal and subsurface properties. A coupled one-dimensional unsaturated-zone and three-dimensional saturated-zone reactive-solute-transport model (PHAST) was used to simulate lengths of phosphorus plumes. Knowledge of phosphorus plume length could facilitate estimates of setback distances for wastewater-infiltration sites from surface water that would be sufficient to protect the surface water from eutrophication caused by phosphorus transport through the subsurface and ultimate discharge to surface water.

The reactive-solute-transport model PHAST was used to simulate ground-water flow, solute transport, equilibrium chemistry for dissolved and sorbed species, and kinetic regulation of organic carbon decomposition and phosphate mineral formation. The phosphorus plume length was defined for the simulations as the maximum extent of the contour for the 0.015 milligram-per-liter concentration of dissolved phosphorus downgradient from the infiltration bed after disposal cessation. Duration of disposal before cessation was assumed to be 50 years into an infiltration bed of 20,000 square feet at the rate of 3 gallons per square foot per day. Time for the maximum extent of the phosphorus plume to develop is on the order of 100 years after disposal cessation. Simulations indicated that phosphorus transport beyond the extent of the 0.015 milligram-per-liter concentration contour was never more than 0.18 kilogram per year, an amount that would likely not alter the ecology of most surface water.

Simulations of phosphorus plume lengths were summarized in a series of response curves. Simulated plume lengths ranged from 200 feet for low phosphorus-concentration effluents (0.25 milligram per liter) and thick (50 feet) unsaturated zones to 3,400 feet for high phosphorus-concentration effluents (14 milligrams per liter) discharged directly into the aquifer (unsaturated-zone thickness of 0 feet). Plume length was nearly independent of unsaturated-zone thickness at phosphorus concentrations in the wastewater that were less than 2 milligrams per liter because little or no phosphorus mineral formed at low phosphorus concentrations. For effluents of high phosphorus concentration, plume length varied from 3,400 feet for unsaturated-zone thickness of 0 to 2,550 feet for unsaturated-zone thickness of 50 feet.

Model treatments of flow and equilibrium-controlled chemistry likely were more accurate than rates of kinetically controlled reactions, notably precipitation of iron-phosphate minerals; the kinetics of such reactions are less well known and thus less well defined in the model. Sensitivity analysis indicated that many chemical and physical aquifer properties, such as hydraulic gradient and model width, did not affect the simulated plume length appreciably, but duration of discharge, size of infiltration bed, amount of dispersion, and number of sorption sites on the aquifer sediments did affect plume length appreciably.

Because simulation of plume length in carbonate-mineral sediments indicated that the plume would be substantially longer than in noncarbonate-mineral sediments, the application of the response curves in locations with carbonate-mineral sediments would be inappropriate. The effect of carbonate minerals in sediments is to increase pH, which causes decreased sorption of phosphorus on aquifer sediments.

Phosphorus removal from solution by precipitation onto aquifer sediments is more efficient at high concentrations of disposed phosphorus than at low concentrations. At very low phosphorus concentrations, the solubility product of phosphorus minerals is not exceeded and no phosphorus mineral forms. An important consequence is that removal of dissolved phosphorus from the plume by processes in the subsurface is decreased the more that removal efforts are applied in treatment before wastewater is disposed.

Model simulations indicate that removal of phosphorus from wastewater disposed through septic systems would have the advantage of efficient phosphorus removal in the subsurface because phosphorus concentrations are high in septic-system effluent. Short plume lengths result from wastewater disposal through septic systems because of the efficient phosphorus removal and because of the low volume of wastewater involved. The simulation results for small-volume systems are not quantitative, however, because wastewater-infiltration rates are much lower than those of the higher-volume system that was used to calibrate the model and to create the plume-length response curves.

The response curves for phosphorus plume lengths, as defined by the maximum extent of the 0.015 milligram-per-liter concentration contour, is clearly defined in the model simulations, although the relation between simulated plume length and protective setback distance is subject to interpretation. Phosphorus does move beyond the point at which the simulated 0.015 milligram-per-liter concentration contour has stopped, so that a determination of protective setback distance must include a consideration of whether that continued flux, or some other flux amount, is appropriate. Also, simulations indicate that phosphorus plumes do not reach their full extent until 50 to 200 years after disposal cessation, depending on concentration of phosphorus disposed. No phosphorus plume has been monitored for that long after cessation, so there is no way to verify the long-term simulation results.




Approach to Computer Simulations of Phosphorus-Plume Length

Conceptual Model

Processes Affecting Phosphorus Transport

Physical Properties

Biogeochemical Processes

Three-Dimensional Reactive-Solute-Transport Model for the Saturated Zone

One-Dimensional Reactive-Solute-Transport Model for the Unsaturated Zone

Combined Unsaturated- and Saturated-Zone Models

Simulation Results for the Saturated- and Unsaturated-Zone Models

Base-Case Saturated-Zone Model and Stages of Plume Development

Sensitivity Analysis

Unsaturated-Zone Model

Response Curves of Phosphorus Plume Length as a Function of Unsaturated-ZoneThickness and Effluent Phosphorus Concentration

Model Verification

Evaluation of Simulation Results

Application of Simulation Results

Model Strengths, Weaknesses, and Reliability

Efficient Use of Phosphorus Removal in the Subsurface

Summary and Conclusions



1–3. Maps showing:

1. Measured dissolved phosphorus concentrations in the aquifer downgradient from sewage infiltration beds at the Massachusetts Military Reservation, Cape Cod, Massachusetts, 1993

2. Distribution of measured concentrations of dissolved phosphorus in ground water approximately 2 feet below the bottom of Ashumet Pond, 1999

3. Extent of nitrate plume emanating from the septic system of the Walden Pond State Reservation

4. Photograph showing sewage-infiltration beds at a new (2002) treatment plant in Acton, permitted for a disposal rate of 0.25 million gallons per day

5. Schematic showing conceptual model of wastewater infiltration through the unsaturated zone from an infiltration bed and transport downgradient through the aquifer

6. Map showing comparative transport of phosphorus and other sewage-derived constituents in the ground-water contaminant plume from wastewater disposal at the Massachusetts Military Reservation, Cape Cod

7. Model grid showing A, Saturated-zone PHAST model grid used in this study; and B, The modeled extent of the dissolved phosphorus plume at year 70 for base case—50 years of continuous discharge—with dissolved phosphorus concentrations shown on a log scale

8, 9. Graphs showing:

8. Base-case unsaturated-zone PHAST model boundaries and grid

9. Solid-phase phosphorus concentrations beneath the infiltration beds at the Massachusetts Military Reservation, Cape Cod

10–16. Graphs showing:

10. Base-case simulations of the stages of phosphorus plume development in the saturated zone

11. Simulated stages of development of the base-case phosphorus plume length (defined as the extent of dissolved phosphorus equal or greater than 0.015 milligram per liter) in the saturated zone

12. Comparison of flux of effluent phosphorus into the infiltration bed and output through the model boundaries from 1,700 to 2,500 feet downgradient

13. Model sensitivity analysis showing base-case phosphorus plume length and plume lengths altered in response to perturbation of the input parameters

14. Phosphorus concentration of effluent entering and exiting the unsaturated zone for simulations of the Walden Pond leachfield and for the base-case conditions

15. Simulated unsaturated-zone concentrations of phosphorus minerals in the solid phase at 10-year intervals during active discharge of wastewater, and of sorbed phosphorus after 10 years

16. Simulated dissolved phosphorus-plume length, as a function of unsaturated- zone thickness and phosphorus concentration in the discharge


1. Solution compositions for uncontaminated ground water and treated sewage effluent

2. Major chemical reactions used in reactive-transport simulations

3. Base-case values for the three-dimensional reactive-transport model and the unsatured zone model

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