# Chapter 6 - Problem 2

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```					Name ____________________       Practical Problems in Groundwater Hydrology             Chapter 6 - Problem 2

1-D CONTAMINANT TRANSPORT OF TCE (CONCENTRATION
VERSUS TIME), ANNE ANDERSON ET AL. VERSUS W.R. GRACE ET
AL., WOBURN, MASSACHUSETTS

Nested monitoring wells at W.R. Grace (left) and "full strength" gallon of TCE (right).
Introduction

This assignment demonstrates how advection, diffusion, dispersion, and chemical retardation
influence the travel velocity and concentration of a TCE plume at Woburn, Massachusetts. Similar
to Problem #1 of this chapter, the Ogata and Banks (1961) analytical solution for one -dimensional
advective transport with dispersion is used (see Chapter 6 in the Reference Book). Using this
equation, you can calculate concentration breakthrough curves at given distances from the source
for TCE contamination.

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.

You will use these parameters to program the Ogata and Banks (1961) equation into the "C vs t"
worksheet to calculate the breakthrough curves of the TCE plume at 800, 1000, and 1200 feet.
Then these breakthrough curves are simulated assuming chemical retardation using a modified
form of the Ogata and Banks (1961) equation in the "C vs t with Retardation" worksheet.

Page 1 of 17                                     Introduction
Name ____________________       Practical Problems in Groundwater Hydrology             Chapter 6 - Problem 2

Instructions - Part I

Determine the concentration of a non-reactive contaminant (no chemical retardation) at three
distances using the one-dimensional advection-dispersion equation developed by Ogata and Banks
(1961) (see Reference Book). To use the ERF and ERFC intrinsic function in EXCEL, you must
have the "Analysis ToolPak" installed as an Add-In. See EXCEL TIPS in the Reference Book for

1. Enter the values of the aquifer and contaminant parameters (K, i, n e, ax, and D*) in the table
provided on the "C vs t" worksheet.

2. Assume the TCE source at the Riley Tannery property is continuously releasing contaminants to
the groundwater flow system at a concentration of 1000 mg/L.

3. Use the "C vs t" worksheet to solve the Ogata-Banks equation in terms of concentration versus
time for specified distances of 800, 1000, and 1200 feet from the source.

4. Using the cells provided on the "C vs t" worksheet, solve for the average linear flow velocity
(vx) and the coefficient of hydrodynamic dispersion (D x) (see Reference Book equations 6-1 and 6-
2).

5. Use a time increment of 100 days between 100 and 2000 days in the first column of the
worksheet. [The smallest time variable is set to 1, instead of zero to avoid division by zero errors in
the worksheet.] The time increments (e.g., 100, 200, 300, etc.) will automatically be reflected into
the time columns for 1000 and 1200 feet.

- First, calculate the argument of the error function based on equation 6-3 in the Reference Book in
cells E16-E36, J16-J36, and O16-O36. The error function values then will change from the initial
values of 1.000 to the correct values based on the argument.

- Next, calculate the concentration (C) and then calculate the relative concentration (C/C 0) for each
of the time periods specified using equation 6-3 in the Reference Book.

6. Repeat the above two steps for the 1000 and 1200 feet portions of the worksheet.

7. Print the concentration versus time table and the breakthrough curves plotted on the " C vs t"
worksheet. Answer the Part I questions that appear on the "Questions" worksheet.

Page 2 of 17                                     Introduction
Name ____________________       Practical Problems in Groundwater Hydrology           Chapter 6 - Problem 2

Instructions - Part II

Compute TCE concentrations in "C vs t" worksheet at the same distances and for the same times
using the same values of hydraulic parameters as in Part I, except use ax values of 10 and 50 feet.
Print the graphs of the breakthrough curves and calculation tables for each dispersivity value.
Answer the questions that appear under Part II of the "Questions" worksheet.

Instructions - Part III

Compute TCE concentrations in the same manner as in Parts I and II of this exercise but modify
the argument of the error function (cells E18-E38, J18-J38, and O18-O38) to account for chemical
retardation, as appears in equation 6-7 in the Reference Book. Use the same parameter values used
in Part I but compute the contaminant velocity (v c) and the retardation factor (R f) for
trichloroethylene (TCE) assuming the dry, bulk density of the soil is 2.00 g/cm 3, and a weight
fraction of organic carbon content equal to 0.60% or 0.006. The partition coefficient between
organic carbon and water (K oc) for TCE is 152 mg/g. Use the "C vs t with Retardation" worksheet
to determine the approximate time when the leading edge of the TCE plume (C/C 0= 0.005) travels
800 feet to well G. Use a starting time of 1 day then 400 days for the second time value and
subsequently at time intervals of 400 days to calculate the concentration curves. Answer the
questions in Part II of the "Questions" worksheet after printing your final breakthrough curve and
concentration versus time table.

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.

Page 3 of 17                                    Introduction
Name ____________________      Practical Problems in Groundwater Hydrology   Chapter 6 - Problem 2

ation of a TCE plume at Woburn, Massachusetts. Similar

am the Ogata and Banks (1961) equation into the "C vs t"

Page 4 of 17                          Introduction
Name ____________________          Practical Problems in Groundwater Hydrology   Chapter 6 - Problem 2

annery property is continuously releasing contaminants to

set to 1, instead of zero to avoid division by zero errors in

in

) for each

Page 5 of 17                         Introduction
Name ____________________        Practical Problems in Groundwater Hydrology   Chapter 6 - Problem 2

" worksheet at the same distances and for the same times

me manner as in Parts I and II of this exercise but modify

water flow and contaminant transport at the Wells G & H

Page 6 of 17                          Introduction
Name ____________________          Practical Problems in Groundwater Hydrology            Chapter 6 - Problem 2

1-D CONTAMINANT TRANSPORT OF TCE (CONCENTRATION
VERSUS TIME), ANNE ANDERSON ET AL. VERSUS W.R. GRACE ET
AL., WOBURN, MASSACHUSETTS

Questions - Part I (4 Total)

Question #1. Compare the concentration versus time curves (breakthrough curves) you calculated
in Part I of this problem (Woburn) with the concentration versus distance curves (concentration
profiles) you produced for Part I in problem 1 (Wooster) of this chapter. What are some of the
similarities and differences between these two types of curves?

Question #2. How long after the contaminant enters the flow system does it take for the leading
edge of the plume (C/C0 = 0.005) to travel from the Riley Tannery property to well G,
approximately 800 ft away? (Print the graph when complete.) [Suggestion: Adjust the time values
until the leading edge reaches 800 ft.]

Question #3. How long will it take the contaminant to travel the 800 feet to well G based solely on
advection? (Show your calculations or demonstrate with a concentration versus distance graph.)

Page 7 of 17                                       Questions
Name ____________________           Practical Problems in Groundwater Hydrology           Chapter 6 - Problem 2

Question #4. How long after the contaminant enters the flow system will it take for the
concentration at well G (800 feet downgradient) to be constant?

Questions - Part II (4 Total)

Question #1. How do differences in ax affect the shape of the breakthrough curves?

Question #2. How do differences in ax affect the arrival time of the leading edge of the
contaminant plume at well G?

Question #3. Compare the answers to the above two questions about the influence of ax to those
you gave for Problem 1, Part II, Questions #1 and #2 in this chapter.

Question #4. How does the change in dispersivity value impact advective front (C/C0 = 0.5) of the
breakthrough curves?

Page 8 of 17                                      Questions
Name ____________________            Practical Problems in Groundwater Hydrology          Chapter 6 - Problem 2

Questions - Part III (3 Total)

Question #1. What is the calculated retardation factor for TCE and how does accounting for
chemical retardation affect the shape of the breakthrough curves?

Question #2. Accounting for the chemical retardation of TCE, when does the leading edge of the
plume (C/C0 = 0.005) arrive at well G? When would the concentration at well G exceed the U.S.
EPA limit of 5 mg/L? [Suggestion: Adjust the time values until the leading edge reaches 800 ft.]

Question #3. Albert Einstein once said that "Everything should be made as simple as possible, but
no simpler." This is a telling quote in light of how one of the plaintiffs' expert witnesses in the
landmark "A Civil Action" trial used the Ogata-Banks equation to obtain arrival times for TCE at
wells G and H, as described in the problem setup material. Based on the geologic cross section you
constructed in Problem 1 in Chapter 1 and the potentiometric map you constructed in Problem 2 in
Chapter 1, what questions would you tell your attorney to pose to this expert on cross examination
if you were the expert witness representing the Riley Tannery, which was owned by Beatrice
Foods? What questions would you tell your attorney if you were the expert witness representing
the Cryovac Plant owned by W.R. Grace?

Page 9 of 17                                     Questions
Name ____________________         Practical Problems in Groundwater Hydrology   Chapter 6 - Problem 2

e graph when complete.) [Suggestion: Adjust the time values

G based solely on

Page 10 of 17                            Questions
Name ____________________   Practical Problems in Groundwater Hydrology   Chapter 6 - Problem 2

= 0.5) of the

Page 11 of 17                            Questions
Name ____________________         Practical Problems in Groundwater Hydrology   Chapter 6 - Problem 2

blem setup material. Based on the geologic cross section you

Page 12 of 17                           Questions
Name ____________________                                                                                                    Practical Problems in Groundwater Hydrology   Chapter 6 - Problem 2

1-D CONTAMINANT TRANSPORT OF TCE (CONCENTRATION VERSUS TIME), ANNE
ANDERSON ET AL. VERSUS W.R. GRACE ET AL., WOBURN, MASSACHUSETTS

Input Parameters
K=    400           ft/day       C0 =   1000       mg/L            x1 =     800      feet
i=  0.001            ft/ft      ax =    50           ft           x2 =    1000      feet
n=    0.30         (decimal)     D* = 1.00E-06    ft2/day          x3 =    1200      feet
2
vx =   1.33          ft/day       Dx =    67       ft /day

Calculations at     800    feet                        Calculations at   1000     feet                        Calculations at   1200     feet
t        C/C0         C       erfc      argument       t        C/C0        C        erfc     argument        t        C/C0        C        erfc   argument
1       0.000        0.0     0.000       48.9081       1       0.000       0.0      0.000      61.1556        1       0.000       0.0      0.000    73.4030
100      0.000        0.0     0.000        4.0825      100      0.000       0.0      0.000       5.3072       100      0.000       0.0      0.000     6.5320
250      0.005        5.3     0.011        1.8074      250      0.000       0.1      0.000       2.5820       250      0.000       0.0      0.000     3.3566
300      0.023       22.8     0.046        1.4142      300      0.001       1.3      0.003       2.1213       300      0.000       0.0      0.000     2.8284
400      0.124      124.1     0.248        0.8165      400      0.022      21.7      0.043       1.4289       400      0.002       1.9      0.004     2.0412
500      0.303      302.8     0.606        0.3651      500      0.098      98.4      0.197       0.9129       500      0.019      19.4      0.039     1.4606
600      0.500      500.0     1.000        0.0000      600      0.240     239.8      0.480       0.5000       600      0.079      78.6      0.157     1.0000
700      0.669      668.7     1.337       -0.3086      700      0.414     413.6      0.827       0.1543       700      0.191     191.4      0.383     0.6172
800      0.793      792.9     1.586       -0.5774      800      0.581     580.9      1.162      -0.1443       800      0.342     341.5      0.683     0.2887
900      0.876      875.9     1.752       -0.8165      900      0.718     718.1      1.436      -0.4082       900      0.500     500.0      1.000     0.0000
1000      0.928      927.9     1.856       -1.0328     1000      0.819     819.3      1.639      -0.6455      1000      0.642     642.5      1.285    -0.2582
1100      0.959      959.1     1.918       -1.2309     1100      0.888     888.5      1.777      -0.8616      1100      0.757     756.9      1.514    -0.4924
1200      0.977      977.2     1.954       -1.4142     1200      0.933     933.2      1.866      -1.0607      1200      0.841     841.3      1.683    -0.7071
1300      0.988      987.5     1.975       -1.5852     1300      0.961     960.9      1.922      -1.2455      1300      0.900     899.9      1.800    -0.9058
1400      0.993      993.2     1.986       -1.7457     1400      0.978     977.6      1.955      -1.4184      1400      0.939     938.6      1.877    -1.0911
1500      0.996      996.4     1.993       -1.8974     1500      0.987     987.3      1.975      -1.5811      1500      0.963     963.2      1.926    -1.2649
1600      0.998      998.1     1.996       -2.0412     1600      0.993     992.9      1.986      -1.7351      1600      0.978     978.3      1.957    -1.4289
1700      0.999      999.0     1.998       -2.1783     1700      0.996     996.1      1.992      -1.8813      1700      0.987     987.5      1.975    -1.5842
1800      0.999      999.5     1.999       -2.3094     1800      0.998     997.9      1.996      -2.0207      1800      0.993     992.8      1.986    -1.7321
1900      1.000      999.7     1.999       -2.4351     1900      0.999     998.8      1.998      -2.1541      1900      0.996     996.0      1.992    -1.8732
2000      1.000      999.8     2.000       -2.5560     2000      0.999     999.4      1.999      -2.2822      2000      0.998     997.7      1.995    -2.0083

ADVECTIVE TRANSPORT WITH DISPERSION AND DIFFUSION TO WELL H

800 feet         1000 feet               1200 feet

1.0

0.9

0.8

0.7

0.6
C / C0

0.5

0.4

0.3

0.2

0.1

0.0
0       200            400              600          800        1000              1200          1400         1600            1800       2000

Page 13 of 17                                C vs t
Name ____________________                                                        Practical Problems in Groundwater Hydrology   Chapter 6 - Problem 2

0.0
0       200            400   600   800      1000       1200   1400   1600    1800          2000
Time (days)

Page 14 of 17                                 C vs t
Name ____________________                 Practical Problems in Groundwater Hydrology   Chapter 6 - Problem 2

Time (days)

Page 15 of 17                                 C vs t
Name ____________________                                                                    Practical Problems in Groundwater Hydrology                                                   Chapter 6 - Problem 2

1-D CONTAMINANT TRANSPORT OF TCE (CONCENTRATION VERSUS TIME), ANNE ANDERSON ET
AL. VERSUS W.R. GRACE ET AL., WOBURN, MASSACHUSETTS

Input Parameters
K=       400        ft/day       C0 =     1000       mg/L        rb =        2.00     g/cm3       Rf =      5.3                x1 =       800      feet
i=     0.001         ft/ft      ax =       25        ft         Koc =       152      mL/g        vc =      0.3      ft/day    x2 =      1000      feet
n=       0.30      (decimal)     D* =    1.0E-06     2
ft /day      foc =      0.006   (decimal)                                  x3 =      1200      feet
vx =      1.3       ft/day       Dx =       33      ft2/day      Kd =       0.912     mL/g

Calculations at     800       feet                  Calculations at        1000    feet                     Calculations at   1200    feet
t       C/C0         C          erfc   argument     t       C/C0             C       erfc     argument      t       C/C0        C       erfc   argument
1      0.000        0.0        0.000   158.984      1      0.000            0.0     0.000     198.743       1      0.000       0.0     0.000   238.502
400     0.000        0.0        0.000    6.946      400     0.000            0.0     0.000      8.934       400     0.000       0.0     0.000    10.922
800     0.000        0.0        0.000    4.200      800     0.000            0.0     0.000      5.606       800     0.000       0.0     0.000     7.011
1200     0.000        0.0        0.000    2.848     1200     0.000            0.0     0.000      3.996      1200     0.000       0.0     0.000     5.144
1680     0.005        5.1        0.010    1.818     1680     0.000            0.0     0.000      2.788      1680     0.000       0.0     0.000     3.758
2000     0.032       32.3        0.065    1.306     2000     0.001            1.0     0.002      2.196      2000     0.000       0.0     0.000     3.085
2400     0.134      134.4        0.269    0.782     2400     0.012           12.1     0.024      1.593      2400     0.000       0.3     0.001     2.405
2800     0.313      313.5        0.627    0.344     2800     0.061           60.7     0.121      1.095      2800     0.005       4.5     0.009     1.846
3200     0.519      519.3        1.039    -0.034    3200     0.172          172.2     0.344      0.669      3200     0.026      26.2     0.052     1.371
3600     0.698      698.4        1.397    -0.368    3600     0.338          338.3     0.677      0.295      3600     0.088      87.8     0.176     0.958
4000     0.827      827.2        1.654    -0.667    4000     0.522          521.6     1.043      -0.038     4000     0.202     201.9     0.404     0.590
4400     0.908      908.0        1.816    -0.939    4400     0.685          684.6     1.369      -0.340     4400     0.357     356.8     0.714     0.260
4800     0.954      953.8        1.908    -1.190    4800     0.808          808.1     1.616      -0.616     4800     0.524     523.6     1.047    -0.042
5200     0.978      977.8        1.956    -1.422    5200     0.891          890.9     1.782      -0.871     5200     0.674     674.2     1.348    -0.319
5600     0.990      989.8        1.980    -1.639    5600     0.941          941.4     1.883      -1.108     5600     0.793     792.6     1.585    -0.577
6000     0.995      995.4        1.991    -1.843    6000     0.970          970.0     1.940      -1.330     6000     0.876     876.0     1.752    -0.817
6400     0.998      998.0        1.996    -2.036    6400     0.985          985.3     1.971      -1.539     6400     0.930     929.8     1.860    -1.042
6800     0.999      999.2        1.998    -2.220    6800     0.993          993.0     1.986      -1.737     6800     0.962     962.1     1.924    -1.255
7200     1.000      999.6        1.999    -2.394    7200     0.997          996.8     1.994      -1.926     7200     0.980     980.3     1.961    -1.457
7600     1.000      999.9        2.000    -2.561    7600     0.999          998.5     1.997      -2.105     7600     0.990     990.1     1.980    -1.649
8000     1.000      999.9        2.000    -2.721    8000     0.999          999.4     1.999      -2.277     8000     0.995     995.2     1.990    -1.832

Advective Transport with Dispersion, Diffusion, and Retardation to Well H

800 feet          1000 feet            1200 feet

1.0

0.9

0.8

0.7

0.6
C / Co

0.5

0.4

0.3

0.2

0.1

0.0
0     500   1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000

Time (days)

Page 16 of 17                                                                  C vs t with Retardation
Name ____________________   Practical Problems in Groundwater Hydrology   Chapter 6 - Problem 2

Page 17 of 17                  C vs t with Retardation

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