A Civil Action - The Woburn Toxic Trial > Learning Modules > 8 - Movement of Contaminants > Contaminant assignment

Learning Module: Subsurface Movement of Contaminants

Module Goals

  • Introduce students to contaminant transport processes including advective, dispersive, diffusive transport and chemical retardation.
  • Introduce students to the mathematical treatment of contaminant transport.
  • Use a data from three sampling events to complete contours of TCE concentrations in the Aberjona River Valley near Wells G & H and explore reasons why TCE concentrations vary for each of the three sampling events.

Student Assignment


Two of the three expert hydrogeologists in the trial constructed contaminant transport models of the groundwater flow system at Wells G and H in order to make predictions backward in time of the arrival times in the two municipal wells of TCE and PCE emanating from the Beatrice property and the W.R. Grace property. These calculations would be used by the court to determine which plaintiffs were exposed to the contaminated water distributed throughout parts of the city. Plaintiffs contracting leukemia before the TCE and PCE from Beatrice and W.R. Grace reached the wells would be released from the lawsuit.

The two experts used vastly different mathematical approaches. One expert used a 1-dimensional equation that required input of average values of permeability, porosity, hydraulic gradient, dispersivity, and chemical retardation. The other expert constructed a 3-dimensional model of the entire flow system that took into account spatial variations in permeability, aquifer thickness, porosity, and hydraulic gradient, and temporal variations in recharge, well pumpage, and streamflow gain/loss. For a more detailed comparison of these approaches, see Bair (2002) (Acrobat (PDF) 4MB Jun18 09).

This assignment is presented in two parts, the first part focuses on creating isoconcentration maps showing the distribution of TCE in the Aberjona River Valley area. The second part of the assignment uses an Excel spreadsheet to calculate the rate of transport of TCE in the Aberjona River River Valley aquifer.

Student Assignment: Part 1-Creating Isoconcentration Maps

This exercise requires contouring of TCE data to evaluatethe aerial distribution and potential sources. Contouring is done in a similar manner to that described in Module 4 Groundwater Hydrology-Constructing Potentiometric Surfaces Wells G & H Superfund Site, Woburn, MA. For this exercise, copies of three maps showing the highest TCE concentration per well from 1979 through 1984, 1985 through 1989 and 1990 through 1993 are used as base maps to be contoured and analyzed. Unlike the instructions in Module 4, students should use content intervals of 10 micrograms per liter (ug/L), 50 ug/L, 100 ug/L and depending on which map is being used, possibly 500 ug/L and 1000 ug/L. Students are advised to start with the highest concentrations and work downward when contouring. It should be noted that many of the monitoring wells were not drilled until after 1984. The absence of monitoring well data (labeled as an NA on the 1979 through 1984 map) should be considered when interpreting the distribution of TCE and answering the questions below. After the data on all three of the maps have been contoured (links to the maps are presented below), students should answer the four questions listed below.

Maximum TCE concentrations from 1978 through 1984 (Acrobat (PDF) 2MB Jul31 09)
Maximum TCE concentrations from 1985 through 1989 (Acrobat (PDF) 2.1MB Jul31 09)
Maximum TCE concentrations from 1990 through 1993 (Acrobat (PDF) 2MB Jul31 09)

Contouring Exercise Questions

  1. Describe the locations of the highest concentrations of TCE for each map. How can this information be attributed to sources of TCE?
  2. Refer to the groundwater contouring exercise in Module 4 and the models of pumping simulations in Module 5. What is the correlation between groundwater flow and TCE distribution?
  3. An additional source of TCE was identified by US EPA after the trial had ended. That additional source was located southeast of the Riley property. Does the distribution of TCE in the three maps provide evidence of this additional source?
  4. Describe the overall distribution of TCE on each of the three maps. How are the distributions similar and different?

Student Assignment: Part 2-Using Excel Spreadsheets to Calculate the Rate of Migration

Background information for this exercise is presented in detail by Bair and Lahm, 2006, Practical Problems in Groundwater Hydrology,Pearson/Prentice Hall, Chapter 6, Problem 2, pp. 6-14 – 6-15. The following summarizes the application of the Excel spreadsheet.


This assignment demonstrates flow processes related to advection, diffusion, dispersion, and chemical retardation's influence the travel velocity and concentration of a TCE plume at Woburn, Massachusetts. It is an analytical solution worksheet in EXCEL format for one-dimensional advective transport with dispersion considered. Using this worksheet, you can calculate concentration breakthrough curves at given times after the release of the source for TCE contamination. The worksheet is presented in the link below. for this exercise, you will insert values for permeability (K) and the initial concentration from the source (Co). The other values are fixed, and the cells are protected so that they cannot be changed. A copy of a typical TCE plume distribution is shown on the image below. This Excel spreadsheet calculation will allow the user to predict when a given concentration will occur at a specific distance from the source or area. The Ogata-Banks formula (see below) is embedded into the Excel spreadsheet to calculate concentration at a specific time.

The Ogata-Banks formula used for the Excel spreadsheet
A contour map showing a typical single source TCE plume

Hydrogeologic data from the unconfined aquifer underlying the Aberjona River valley at Woburn indicate that the aquifer has a hydraulic conductivity of 400 ft/d, an effective porosity of 30% (Metheny, 2004), and an average hydraulic gradient of 0.001 (Myette et al., 1982). The longitudinal dispersivity (ax) is assumed to be 25 ft. and the coefficient of molecular diffusion is assumed to be 1x10-6 ft2/d. For this assignment you'll use a permeability value of 400 f/d (K) and and C0 of 1000 ug/l. The cells on the Ogata-Banks Excel spreadsheet calculator where this data is to be entered are highlighted in light blue. The other values are protected, so they do not need to be changed.

The spreadsheet uses error function and the complementary error function. When you open the spreadsheet, if you receive a "#NAME?" error statement listed under the ERFC column, it's likely that you do not have the Analysis Toolpack installed. To utilize these functions in the attached Excelspreadsheet you must add them. Go to the Tools tab and open the menu. Select Add-Ins, and from the Add-Ins available menu, select the Analysis Toolpack and click OK. If the analysis Toolpack is not highlighted when you open the menu, you may have to load the original Excel CD and download this feature.

Ogata-Banks Excel spreadsheet calculator (Excel 67kB Aug6 09)

These parameters have been programmed into the spreadsheet using the Ogata and Banks (1961) equation reference Runkel, 1996. The "C vs t" worksheet calculates the breakthrough curves of the TCE plume at 800, 1000, and 1200 feet and assumes no retardation of TCE movement (related to absorption or degradation) within the aquifer. These breakthrough curves are recalculated on the second spreadsheet tabbed "C vs t with Retardation", which assumes chemical retardation using a modified form of the Ogata and Banks (1961) equation. You will enter the same K and C0 values on the spreadsheet tabbed "C vs t with Retardation". When the data is entered, the table below the input parameters will populate showing time intervals (column t), the calculated ratio for the concentration at time t per initial concentration (C/C0) at a defined distance from the source, the concentration for a specific time t (C) at a defined distance from the source and the values for the complementary error function and its argument. The table is repeated in three sets of columns with each set of columns representing the distances of 800 feet, 1000 feet and 1200 feet from the source. The values from the table are plotted on a graph immediately below. The graph shows the ratio of C/C0, which is the concentration at a given time at a fixed distance (800, 1000 or 1200 feet from the source). From the graph one can determine how long it will take a given concentration to occur specific fixed distance. This type of calculation would be valuable in estimating the time of arrival of a contamination plume from a given source. The accuracy of this time is dependent on the homogeneity of the aquifer media in the amount of retardation by organic material in the aquifer.

After you have entered the K and C0 data into the spreadsheet, answer the series of questions listed below.

TCE rate of migration Questions

  1. If the concentration of the maximum contaminant level (MCL) for TCE is 5 ug/l, at what time would that concentration be exceeded at each the 800 feet location, the 1000 feet location, and the 1200 feet location? Use the "c vs t" tabbed worksheet for your answer.
  2. Using the "c vs t with retardation" tabbed worksheet for your answer, determine the time when the TCE concentration exceeds the MCL at each the 800 feet location, the 1000 feet location, and the 1200 feet location? Explain why there are differences in these times.
  3. Using the "c vs t with retardation" tabbed worksheet, change the C0 value to 500 ug/l. How does this change the shape of the graph? Why?
  4. Using the "c vs t with retardation" tabbed worksheet, change the K value to 200 f/d. How does this change the shape of the graph? Why?
  5. Using the same worksheet as specified in number 4 above, reset the K value to 400 f/d and C0 value to 1000 ug/l then change the 800 feet distance to 400 feet. At what time does the C value exceed 5 ug/l? Remember, the y-axis represents C/C0 values and C0 is assumed to be constant.
  6. How could a tool such as this Excel spreadsheet been used to present scientific evidence regarding the migration of TCE to Wells G & H? Keep in mind, computing capabilities in the mid-1980s were much less than what you are utilizing now. Refer to Technological Context of the 1986 Trial.
  7. George Pinder, the plaintiffs groundwater expert used a model similar to the one programmed into this Excel spreadsheet. Knowing that this model assumes the subsurface is infinitely isotropic and homogenous, how would the defense discredit the estimate of arrival time using this type of model? Use the cross-section prepared as part of Module 3 to describe why variation of the lithology is important to understanding groundwater flow in the Aberjona River Valley.

Resources for TCE fate and transport transport

Introduction to Groundwater Hydraulics, USGS, 2005
Bibliography of USGS articles regarding chlorinated solvent patent transport
Fate and Transport Modeling of Selected Chlorinated Organic Compunds at Hangar 1000, U.S. Naval Air Station, Jacksonville, Florida USGS, 2003

Additional References

Metheny, M. 2004. Evaluation of groundwater flow and contaminant transport at the Wells G & H Superfund Site, Woburn, Massachusetts, from 1960 to 1986 and estimation of TCE and PCE concentrations delivered to Woburn residences. Doctor of Philosophy, Ohio State University, Geological Sciences. 367p.

Myette, C.F., D.G. Johnson, J.C. Olimpio. 1987. Area of influence and zone of contribution to superfund site wells G and H, Woburn, Massachusetts. U.S. Geological Survey, Water-Resources Investigations 87-4100. 86p.

Ogata, A. and R.B. Banks, 1961, A solution of the differential equation of longitudinal dispersion in porous media, U.S. Geological Survey Professional Paper 411-A.

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